Solve by Completing the Square x^2-12x=61

$x^{2} - 12 x = 61$

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.

$x^{2} - 12 x + {(- 6)}^{2} = 61 + {(- 6)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

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

$x^{2} - 12 x + 36 = 61 + {(- 6)}^{2}$

Simplify the right side.

Simplify $61 + {(- 6)}^{2}$ .

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

$x^{2} - 12 x + 36 = 61 + 36$

Add $61$ and $36$ .

$x^{2} - 12 x + 36 = 97$

Step 4

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

${(x - 6)}^{2} = 97$

Step 5

Solve the equation for $x$ .

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

$x - 6 = \pm \sqrt{97}$

Add $6$ to both sides of the equation.

$x = \pm \sqrt{97} + 6$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{97} + 6$

Decimal Form:

$x = 15.84885780 \dots, - 3.84885780 \dots$