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

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

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 $b$ .

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

Step 2

Add the term to each side of the equation.

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

Step 3

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 4

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

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

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.

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

Subtract $11$ from both sides of the equation.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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