Solve by Completing the Square x^2=18x+40

$x^{2} = 18 x + 40$

Step 1

Subtract $18 x$ from both sides of the equation.

$x^{2} - 18 x = 40$

Step 2

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 3

Add the term to each side of the equation.

$x^{2} - 18 x + {(- 9)}^{2} = 40 + {(- 9)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} - 18 x + 81 = 40 + {(- 9)}^{2}$

Simplify the right side.

Simplify $40 + {(- 9)}^{2}$ .

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

$x^{2} - 18 x + 81 = 40 + 81$

Add $40$ and $81$ .

$x^{2} - 18 x + 81 = 121$

Step 5

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

${(x - 9)}^{2} = 121$

Step 6

Solve the equation for $x$ .

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

$x - 9 = \pm \sqrt{121}$

Simplify $\pm \sqrt{121}$ .

Rewrite $121$ as $11^{2}$ .

$x - 9 = \pm \sqrt{11^{2}}$

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

$x - 9 = \pm 11$

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.

$x - 9 = 11$

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

Add $9$ to both sides of the equation.

$x = 11 + 9$

Add $11$ and $9$ .

$x = 20$

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

$x - 9 = - 11$

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

Add $9$ to both sides of the equation.

$x = - 11 + 9$

Add $- 11$ and $9$ .

$x = - 2$

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

$x = 20, - 2$

Solve by Completing the Square x^2=18x+40

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