Solve by Completing the Square x^2+24x=33

$x^{2} + 24 x = 33$

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.

$x^{2} + 24 x + {(12)}^{2} = 33 + {(12)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

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

$x^{2} + 24 x + 144 = 33 + {(12)}^{2}$

Simplify the right side.

Simplify $33 + {(12)}^{2}$ .

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

$x^{2} + 24 x + 144 = 33 + 144$

Add $33$ and $144$ .

$x^{2} + 24 x + 144 = 177$

Step 4

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

${(x + 12)}^{2} = 177$

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.

$x + 12 = \pm \sqrt{177}$

Subtract $12$ from both sides of the equation.

$x = \pm \sqrt{177} - 12$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{177} - 12$

Decimal Form:

$x = 1.30413469 \dots, - 25.30413469 \dots$