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

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

Step 1

Subtract $x^{2}$ from both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot - 1 \cdot - 24}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot - 24$ .

Multiply $- 4$ by $- 1$ .

$x = \frac{- 10 \pm \sqrt{100 + 4 \cdot - 24}}{2 \cdot - 1}$

Multiply $4$ by $- 24$ .

$x = \frac{- 10 \pm \sqrt{100 - 96}}{2 \cdot - 1}$

Subtract $96$ from $100$ .

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

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

$x = \frac{- 10 \pm \sqrt{2^{2}}}{2 \cdot - 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 10 \pm 2}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{- 10 \pm 2}{- 2}$

Simplify $\frac{- 10 \pm 2}{- 2}$ .

$x = 5 \pm 1$

Step 5

The final answer is the combination of both solutions.

$x = 6, 4$