Solve by Completing the Square x^2-18x=-80

$x^{2} - 18 x = - 80$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 9)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} - 18 x + {(- 9)}^{2} = - 80 + {(- 9)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $- 9$ to the power of $2$ .

$x^{2} - 18 x + 81 = - 80 + {(- 9)}^{2}$

Simplify the right side.

Simplify $- 80 + {(- 9)}^{2}$ .

Raise $- 9$ to the power of $2$ .

$x^{2} - 18 x + 81 = - 80 + 81$

Add $- 80$ and $81$ .

$x^{2} - 18 x + 81 = 1$

Step 4

Factor the perfect trinomial square into ${(x - 9)}^{2}$ .

${(x - 9)}^{2} = 1$

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.

$x - 9 = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x - 9 = \pm 1$

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.

$x - 9 = 1$

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

Add $9$ to both sides of the equation.

$x = 1 + 9$

Add $1$ and $9$ .

$x = 10$

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

$x - 9 = - 1$

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

Add $9$ to both sides of the equation.

$x = - 1 + 9$

Add $- 1$ and $9$ .

$x = 8$

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

$x = 10, 8$