Solve by Completing the Square x^2=24x+10

$x^{2} = 24 x + 10$

Step 1

Subtract $24 x$ from both sides of the equation.

$x^{2} - 24 x = 10$

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 $b$ .

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

Step 3

Add the term to each side of the equation.

$x^{2} - 24 x + {(- 12)}^{2} = 10 + {(- 12)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

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

$x^{2} - 24 x + 144 = 10 + {(- 12)}^{2}$

Simplify the right side.

Simplify $10 + {(- 12)}^{2}$ .

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

$x^{2} - 24 x + 144 = 10 + 144$

Add $10$ and $144$ .

$x^{2} - 24 x + 144 = 154$

Step 5

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

${(x - 12)}^{2} = 154$

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.

$x - 12 = \pm \sqrt{154}$

Add $12$ to both sides of the equation.

$x = \pm \sqrt{154} + 12$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{154} + 12$

Decimal Form:

$x = 24.40967364 \dots, - 0.40967364 \dots$