Solve by Completing the Square p^2+16p-22=0

$p^{2} + 16 p - 22 = 0$

Step 1

Add $22$ to both sides of the equation.

$p^{2} + 16 p = 22$

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 $b$ .

${(\frac{b}{2})}^{2} = {(8)}^{2}$

Step 3

Add the term to each side of the equation.

$p^{2} + 16 p + {(8)}^{2} = 22 + {(8)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $8$ to the power of $2$ .

$p^{2} + 16 p + 64 = 22 + {(8)}^{2}$

Simplify the right side.

Simplify $22 + {(8)}^{2}$ .

Raise $8$ to the power of $2$ .

$p^{2} + 16 p + 64 = 22 + 64$

Add $22$ and $64$ .

$p^{2} + 16 p + 64 = 86$

Step 5

Factor the perfect trinomial square into ${(p + 8)}^{2}$ .

${(p + 8)}^{2} = 86$

Step 6

Solve the equation for $p$ .

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

$p + 8 = \pm \sqrt{86}$

Subtract $8$ from both sides of the equation.

$p = \pm \sqrt{86} - 8$

Step 7

The result can be shown in multiple forms.

Exact Form:

$p = \pm \sqrt{86} - 8$

Decimal Form:

$p = 1.27361849 \dots, - 17.27361849 \dots$