Solve by Completing the Square x^2-12x=8

$x^{2} - 12 x = 8$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 6)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} - 12 x + {(- 6)}^{2} = 8 + {(- 6)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $- 6$ to the power of $2$ .

$x^{2} - 12 x + 36 = 8 + {(- 6)}^{2}$

Simplify the right side.

Simplify $8 + {(- 6)}^{2}$ .

Raise $- 6$ to the power of $2$ .

$x^{2} - 12 x + 36 = 8 + 36$

Add $8$ and $36$ .

$x^{2} - 12 x + 36 = 44$

Step 4

Factor the perfect trinomial square into ${(x - 6)}^{2}$ .

${(x - 6)}^{2} = 44$

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.

$x - 6 = \pm \sqrt{44}$

Simplify $\pm \sqrt{44}$ .

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$x - 6 = \pm \sqrt{4 (11)}$

Rewrite $4$ as $2^{2}$ .

$x - 6 = \pm \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$x - 6 = \pm 2 \sqrt{11}$

Add $6$ to both sides of the equation.

$x = \pm 2 \sqrt{11} + 6$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{11} + 6$

Decimal Form:

$x = 12.63324958 \dots, - 0.63324958 \dots$