Solve Using the Quadratic Formula x(x-4)=32

$x (x - 4) = 32$

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Simplify $x (x - 4)$ .

Apply the distributive property.

$x \cdot x + x \cdot - 4 = 32$

Simplify the expression.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 = 32$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 x = 32$

Subtract $32$ from both sides of the equation.

$x^{2} - 4 x - 32 = 0$

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 $a = 1$ , $b = - 4$ , and $c = - 32$ into the quadratic formula and solve for $x$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (1 \cdot - 32)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 4$ to the power of $2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 1 \cdot - 32}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 32$ .

Multiply $- 4$ by $1$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot - 32}}{2 \cdot 1}$

Multiply $- 4$ by $- 32$ .

$x = \frac{4 \pm \sqrt{16 + 128}}{2 \cdot 1}$

Add $16$ and $128$ .

$x = \frac{4 \pm \sqrt{144}}{2 \cdot 1}$

Rewrite $144$ as $12^{2}$ .

$x = \frac{4 \pm \sqrt{12^{2}}}{2 \cdot 1}$

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

$x = \frac{4 \pm 12}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{4 \pm 12}{2}$

Simplify $\frac{4 \pm 12}{2}$ .

$x = 2 \pm 6$

Step 5

The final answer is the combination of both solutions.

$x = 8, - 4$