Solve Using the Quadratic Formula 8x=x^2-9

$8 x = x^{2} - 9$

Step 1

Move all the expressions to the left side of the equation.

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

$8 x - x^{2} = - 9$

Add $9$ to both sides of the equation.

$8 x - x^{2} + 9 = 0$

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 $a = - 1$ , $b = 8$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (- 1 \cdot 9)}}{2 \cdot - 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $8$ to the power of $2$ .

$x = \frac{- 8 \pm \sqrt{64 - 4 \cdot - 1 \cdot 9}}{2 \cdot - 1}$

Multiply $- 4 \cdot - 1 \cdot 9$ .

Multiply $- 4$ by $- 1$ .

$x = \frac{- 8 \pm \sqrt{64 + 4 \cdot 9}}{2 \cdot - 1}$

Multiply $4$ by $9$ .

$x = \frac{- 8 \pm \sqrt{64 + 36}}{2 \cdot - 1}$

Add $64$ and $36$ .

$x = \frac{- 8 \pm \sqrt{100}}{2 \cdot - 1}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{- 8 \pm \sqrt{10^{2}}}{2 \cdot - 1}$

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

$x = \frac{- 8 \pm 10}{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x = \frac{- 8 \pm 10}{- 2}$

Simplify $\frac{- 8 \pm 10}{- 2}$ .

$x = 4 \pm 5$

Step 5

The final answer is the combination of both solutions.

$x = 9, - 1$