Solve by Completing the Square x^2+24x=17

$x^{2} + 24 x = 17$

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 $b$ .

${(\frac{b}{2})}^{2} = {(12)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} + 24 x + {(12)}^{2} = 17 + {(12)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $12$ to the power of $2$ .

$x^{2} + 24 x + 144 = 17 + {(12)}^{2}$

Simplify the right side.

Simplify $17 + {(12)}^{2}$ .

Raise $12$ to the power of $2$ .

$x^{2} + 24 x + 144 = 17 + 144$

Add $17$ and $144$ .

$x^{2} + 24 x + 144 = 161$

Step 4

Factor the perfect trinomial square into ${(x + 12)}^{2}$ .

${(x + 12)}^{2} = 161$

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.

$x + 12 = \pm \sqrt{161}$

Subtract $12$ from both sides of the equation.

$x = \pm \sqrt{161} - 12$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{161} - 12$

Decimal Form:

$x = 0.68857754 \dots, - 24.68857754 \dots$