Solve Using the Quadratic Formula x^2-16x=-63

$x^{2} - 16 x = - 63$

Step 1

Add $63$ to both sides of the equation.

$x^{2} - 16 x + 63 = 0$

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 $a = 1$ , $b = - 16$ , and $c = 63$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (1 \cdot 63)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 1 \cdot 63}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 63$ .

Multiply $- 4$ by $1$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 63}}{2 \cdot 1}$

Multiply $- 4$ by $63$ .

$x = \frac{16 \pm \sqrt{256 - 252}}{2 \cdot 1}$

Subtract $252$ from $256$ .

$x = \frac{16 \pm \sqrt{4}}{2 \cdot 1}$

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

$x = \frac{16 \pm \sqrt{2^{2}}}{2 \cdot 1}$

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

$x = \frac{16 \pm 2}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{16 \pm 2}{2}$

Simplify $\frac{16 \pm 2}{2}$ .

$x = 8 \pm 1$

Step 5

The final answer is the combination of both solutions.

$x = 9, 7$