Algebra Examples

4 x^{2} - 8 x - 12 = 0

$4 x^{2} - 8 x - 12 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

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

Step 2

Substitute the values

a = 4

$a = 4$ ,

b = - 8

$b = - 8$ , and

c = - 12

$c = - 12$ into the quadratic formula and solve for

x

$x$ .

\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (4 \cdot - 12)}}{2 \cdot 4}

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (4 \cdot - 12)}}{2 \cdot 4}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Raise

- 8

$- 8$ to the power of

2

$2$ .

x = \frac{8 \pm \sqrt{64 - 4 \cdot 4 \cdot - 12}}{2 \cdot 4}

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 4 \cdot - 12}}{2 \cdot 4}$

Step 3.1.2

Multiply

- 4 \cdot 4 \cdot - 12

$- 4 \cdot 4 \cdot - 12$ .

Tap for more steps...

Step 3.1.2.1

Multiply

- 4

$- 4$ by

4

$4$ .

x = \frac{8 \pm \sqrt{64 - 16 \cdot - 12}}{2 \cdot 4}

$x = \frac{8 \pm \sqrt{64 - 16 \cdot - 12}}{2 \cdot 4}$

Step 3.1.2.2

Multiply

- 16

$- 16$ by

- 12

$- 12$ .

x = \frac{8 \pm \sqrt{64 + 192}}{2 \cdot 4}

$x = \frac{8 \pm \sqrt{64 + 192}}{2 \cdot 4}$

x = \frac{8 \pm \sqrt{64 + 192}}{2 \cdot 4}

$x = \frac{8 \pm \sqrt{64 + 192}}{2 \cdot 4}$

Step 3.1.3

Add

64

$64$ and

192

$192$ .

x = \frac{8 \pm \sqrt{256}}{2 \cdot 4}

$x = \frac{8 \pm \sqrt{256}}{2 \cdot 4}$

Step 3.1.4

Rewrite

256

$256$ as

16^{2}

$16^{2}$ .

x = \frac{8 \pm \sqrt{16^{2}}}{2 \cdot 4}

$x = \frac{8 \pm \sqrt{16^{2}}}{2 \cdot 4}$

Step 3.1.5

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

x = \frac{8 \pm 16}{2 \cdot 4}

$x = \frac{8 \pm 16}{2 \cdot 4}$

x = \frac{8 \pm 16}{2 \cdot 4}

$x = \frac{8 \pm 16}{2 \cdot 4}$

Step 3.2

Multiply

2

$2$ by

4

$4$ .

x = \frac{8 \pm 16}{8}

$x = \frac{8 \pm 16}{8}$

Step 3.3

Simplify

\frac{8 \pm 16}{8}

$\frac{8 \pm 16}{8}$ .

x = 1 \pm 2

$x = 1 \pm 2$

x = 1 \pm 2

$x = 1 \pm 2$

Step 4

The final answer is the combination of both solutions.

x = 3, - 1

$x = 3, - 1$