Solve by Completing the Square x^2=22x+10

$x^{2} = 22 x + 10$

Step 1

Subtract $22 x$ from both sides of the equation.

$x^{2} - 22 x = 10$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 11)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 22 x + {(- 11)}^{2} = 10 + {(- 11)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 11$ to the power of $2$ .

$x^{2} - 22 x + 121 = 10 + {(- 11)}^{2}$

Simplify the right side.

Simplify $10 + {(- 11)}^{2}$ .

Raise $- 11$ to the power of $2$ .

$x^{2} - 22 x + 121 = 10 + 121$

Add $10$ and $121$ .

$x^{2} - 22 x + 121 = 131$

Step 5

Factor the perfect trinomial square into ${(x - 11)}^{2}$ .

${(x - 11)}^{2} = 131$

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.

$x - 11 = \pm \sqrt{131}$

Add $11$ to both sides of the equation.

$x = \pm \sqrt{131} + 11$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{131} + 11$

Decimal Form:

$x = 22.44552314 \dots, - 0.44552314 \dots$