Algebra Examples

4 x^{2} - 64 = 0

$4 x^{2} - 64 = 0$

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 = 0

$b = 0$ , and

c = - 64

$c = - 64$ into the quadratic formula and solve for

x

$x$ .

\frac{0 \pm \sqrt{0^{2} - 4 \cdot (4 \cdot - 64)}}{2 \cdot 4}

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (4 \cdot - 64)}}{2 \cdot 4}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

Raising

0

$0$ to any positive power yields

0

$0$ .

x = \frac{0 \pm \sqrt{0 - 4 \cdot 4 \cdot - 64}}{2 \cdot 4}

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 4 \cdot - 64}}{2 \cdot 4}$

Step 3.1.2

Multiply

- 4 \cdot 4 \cdot - 64

$- 4 \cdot 4 \cdot - 64$ .

Tap for more steps...

Step 3.1.2.1

Multiply

- 4

$- 4$ by

4

$4$ .

x = \frac{0 \pm \sqrt{0 - 16 \cdot - 64}}{2 \cdot 4}

$x = \frac{0 \pm \sqrt{0 - 16 \cdot - 64}}{2 \cdot 4}$

Step 3.1.2.2

Multiply

- 16

$- 16$ by

- 64

$- 64$ .

x = \frac{0 \pm \sqrt{0 + 1024}}{2 \cdot 4}

$x = \frac{0 \pm \sqrt{0 + 1024}}{2 \cdot 4}$

x = \frac{0 \pm \sqrt{0 + 1024}}{2 \cdot 4}

$x = \frac{0 \pm \sqrt{0 + 1024}}{2 \cdot 4}$

Step 3.1.3

Add

0

$0$ and

1024

$1024$ .

x = \frac{0 \pm \sqrt{1024}}{2 \cdot 4}

$x = \frac{0 \pm \sqrt{1024}}{2 \cdot 4}$

Step 3.1.4

Rewrite

1024

$1024$ as

32^{2}

$32^{2}$ .

x = \frac{0 \pm \sqrt{32^{2}}}{2 \cdot 4}

$x = \frac{0 \pm \sqrt{32^{2}}}{2 \cdot 4}$

Step 3.1.5

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

x = \frac{0 \pm 32}{2 \cdot 4}

$x = \frac{0 \pm 32}{2 \cdot 4}$

x = \frac{0 \pm 32}{2 \cdot 4}

$x = \frac{0 \pm 32}{2 \cdot 4}$

Step 3.2

Multiply

2

$2$ by

4

$4$ .

x = \frac{0 \pm 32}{8}

$x = \frac{0 \pm 32}{8}$

Step 3.3

Simplify

\frac{0 \pm 32}{8}

$\frac{0 \pm 32}{8}$ .

x = \pm 4

$x = \pm 4$

x = \pm 4

$x = \pm 4$

Step 4

The final answer is the combination of both solutions.

x = 4, - 4

$x = 4, - 4$