Solve by Completing the Square x^2-24x=-80

$x^{2} - 24 x = - 80$

Step 1

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 12)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} - 24 x + {(- 12)}^{2} = - 80 + {(- 12)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $- 12$ to the power of $2$ .

$x^{2} - 24 x + 144 = - 80 + {(- 12)}^{2}$

Simplify the right side.

Simplify $- 80 + {(- 12)}^{2}$ .

Raise $- 12$ to the power of $2$ .

$x^{2} - 24 x + 144 = - 80 + 144$

Add $- 80$ and $144$ .

$x^{2} - 24 x + 144 = 64$

Step 4

Factor the perfect trinomial square into ${(x - 12)}^{2}$ .

${(x - 12)}^{2} = 64$

Step 5

Solve the equation for $x$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x - 12 = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$x - 12 = \pm \sqrt{8^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x - 12 = \pm 8$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 12 = 8$

Move all terms not containing $x$ to the right side of the equation.

Add $12$ to both sides of the equation.

$x = 8 + 12$

Add $8$ and $12$ .

$x = 20$

Next, use the negative value of the $\pm$ to find the second solution.

$x - 12 = - 8$

Move all terms not containing $x$ to the right side of the equation.

Add $12$ to both sides of the equation.

$x = - 8 + 12$

Add $- 8$ and $12$ .

$x = 4$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 20, 4$

Solve by Completing the Square x^2-24x=-80

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