Solve Using the Quadratic Formula x^2+24x=10

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

Step 1

Subtract $10$ from both sides of the equation.

$x^{2} + 24 x - 10 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 24$ , and $c = - 10$ into the quadratic formula and solve for $x$ .

$\frac{- 24 \pm \sqrt{24^{2} - 4 \cdot (1 \cdot - 10)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $24$ to the power of $2$ .

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot 1 \cdot - 10}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 10$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot - 10}}{2 \cdot 1}$

Multiply $- 4$ by $- 10$ .

$x = \frac{- 24 \pm \sqrt{576 + 40}}{2 \cdot 1}$

Add $576$ and $40$ .

$x = \frac{- 24 \pm \sqrt{616}}{2 \cdot 1}$

Rewrite $616$ as $2^{2} \cdot 154$ .

Factor $4$ out of $616$ .

$x = \frac{- 24 \pm \sqrt{4 (154)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 24 \pm \sqrt{2^{2} \cdot 154}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 24 \pm 2 \sqrt{154}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 24 \pm 2 \sqrt{154}}{2}$

Simplify $\frac{- 24 \pm 2 \sqrt{154}}{2}$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

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