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- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_for_Science_Technology_Engineering_and_Mathematics_(Diaz)/11%3A_Quadratic_Equations_and_Applications/11.02%3A_Completing_the_SquareRewrite the quadratic equation so that the coefficient of the leading term is one, and the original constant coefficient is on the opposite side of the equal sign from the leading and linear terms. \[...Rewrite the quadratic equation so that the coefficient of the leading term is one, and the original constant coefficient is on the opposite side of the equal sign from the leading and linear terms. \[\begin{aligned} 3x^2-36x+60&=0 \\ 3x^2-36x&=-60 \\ \color{blue}{3}\color{black}{(}x^2-12x)&=\color{blue}{3}\color{black}{\cdot}-20 \\ \color{black}{\cancel{\color{blue}{3}}}\color{black}{(}x^2-12x)&=\color{black}{\cancel{\color{blue}{3}}}\color{black}{\cdot}-20 \\ x^2-12x&=-20\end{aligned}\]
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Arnold)/08%3A_Quadratic_Functions/8.03%3A_Completing_the_SquareSelect 2:zero from the CALC menu, move the cursor slightly to the left of the first \(x\)-intercept and press ENTER in response to “Left bound.” Move the cursor slightly to the right of the first \(x\)-...Select 2:zero from the CALC menu, move the cursor slightly to the left of the first \(x\)-intercept and press ENTER in response to “Left bound.” Move the cursor slightly to the right of the first \(x\)-intercept and press ENTER in response to “Right bound.” Leave the cursor where it sits and press ENTER in response to “Guess.” The calculator responds by finding the \(x\)-coordinate of the \(x\)-intercept, as shown in the first image in Figure \(\PageIndex{6}\).
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/02%3A_Linear_and_Quadratic_Functions/2.03%3A_Quadratic_FunctionsYou may recall studying quadratic equations in Intermediate Algebra. In this section, we review those equations in the context of our next family of functions: the quadratic functions.
- https://math.libretexts.org/Courses/Hope_College/Math_125%3A_Hope_College/01%3A_Algebra_Essentials/1.09%3A_Quadratic_EquationsMany quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find soluti...Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
- https://math.libretexts.org/Courses/Mission_College/Math_1X%3A_College_Algebra_w__Support_(Sklar)/01%3A_Linear_and_Quadratic_Functions/1.03%3A_Solving_Quadratic_EquationsMany quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find soluti...Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
- https://math.libretexts.org/Workbench/College_Algebra_2e_(OpenStax)/02%3A_Equations_and_Inequalities/2.06%3A_Quadratic_EquationsMany quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find soluti...Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
- https://math.libretexts.org/Courses/Coastline_College/Math_C115%3A_College_Algebra_(Tran)/02%3A_Equations_and_Inequalities/2.06%3A_Quadratic_EquationsMany quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find soluti...Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
- https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/02%3A_Equations_and_Inequalities/2.06%3A_Quadratic_EquationsMany quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find soluti...Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Ellis_and_Burzynski)/10%3A_Quadratic_Equations/10.05%3A_Solving_Quadratic_Equations_Using_the_Method_of_Completing_the_SquareWe need another method for solving quadratic equations. The method we shall study is based on perfect square trinomials and extraction of roots. The method is called solving quadratic equations by co...We need another method for solving quadratic equations. The method we shall study is based on perfect square trinomials and extraction of roots. The method is called solving quadratic equations by completing the square.
- https://math.libretexts.org/Bookshelves/Precalculus/APEX_PreCalculus_(Chapman_Herald_and_Libertini)/02%3A_Basic_Skills_for_Calculus/2.05%3A_Completing_the_SquareBy factoring out the 4, \(x^2\) will have a coefficient of 1 and we can work like we did in our earlier examples. \[\begin{align}\begin{aligned}\begin{split} f(x) = 4x^2+12x-3 & = 4 \Bigg[x^2 + 3x-\fr...By factoring out the 4, \(x^2\) will have a coefficient of 1 and we can work like we did in our earlier examples. \[\begin{align}\begin{aligned}\begin{split} f(x) = 4x^2+12x-3 & = 4 \Bigg[x^2 + 3x-\frac{3}{4} \Bigg] \\ & = 4 \Bigg[x^2 + 2\bigg( \frac{3}{2} \bigg)x + \bigg( \frac{3}{2} \bigg)^2 - \bigg( \frac{3}{2} \bigg)^2 -\frac{3}{4} \Bigg] \\ & = 4 \Bigg[ \bigg( x + \frac{3}{2} \bigg)^2 - \frac{9}{4} - \frac{3}{4} \Bigg] \\ & = 4 \Bigg[\bigg( x + \frac{3}{2} \bigg)^2 - \frac{12}{4}\Bigg] \\ …
- https://math.libretexts.org/Courses/Chabot_College/Chabot_College_College_Algebra_for_BSTEM/02%3A_Equations_and_Inequalities/2.05%3A_Quadratic_EquationsMany quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find soluti...Many quadratic equations can be solved by factoring when the equation has a leading coefficient of 1 or if the equation is a difference of squares. The zero-factor property is then used to find solutions. Many quadratic equations with a leading coefficient other than 1 can be solved by factoring using the grouping method. Another method for solving quadratics is the square root property. The variable is squared. We isolate the squared term and take the square root of both sides of the equation.
