Solve Using the Quadratic Formula 4x^2+28x-32=0

$4 x^{2} + 28 x - 32 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 4$ , $b = 28$ , and $c = - 32$ into the quadratic formula and solve for $x$ .

$\frac{- 28 \pm \sqrt{28^{2} - 4 \cdot (4 \cdot - 32)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $28$ to the power of $2$ .

$x = \frac{- 28 \pm \sqrt{784 - 4 \cdot 4 \cdot - 32}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{- 28 \pm \sqrt{784 - 16 \cdot - 32}}{2 \cdot 4}$

Multiply $- 16$ by $- 32$ .

$x = \frac{- 28 \pm \sqrt{784 + 512}}{2 \cdot 4}$

Add $784$ and $512$ .

$x = \frac{- 28 \pm \sqrt{1296}}{2 \cdot 4}$

Rewrite $1296$ as $36^{2}$ .

$x = \frac{- 28 \pm \sqrt{36^{2}}}{2 \cdot 4}$

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

$x = \frac{- 28 \pm 36}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 28 \pm 36}{8}$

Simplify $\frac{- 28 \pm 36}{8}$ .

$x = \frac{- 7 \pm 9}{2}$

Step 4

The final answer is the combination of both solutions.

$x = 1, - 8$