Algebra Examples

x^{2} = 64

$x^{2} = 64$

Step 1

Subtract

64

$64$ from both sides of the equation.

x^{2} - 64 = 0

$x^{2} - 64 = 0$

Step 2

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 3

Substitute the values

a = 1

$a = 1$ ,

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 (1 \cdot - 64)}}{2 \cdot 1}

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 64)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising

0

$0$ to any positive power yields

0

$0$ .

x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 64}}{2 \cdot 1}

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 64}}{2 \cdot 1}$

Step 4.1.2

Multiply

- 4 \cdot 1 \cdot - 64

$- 4 \cdot 1 \cdot - 64$ .

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Step 4.1.2.1

Multiply

- 4

$- 4$ by

1

$1$ .

x = \frac{0 \pm \sqrt{0 - 4 \cdot - 64}}{2 \cdot 1}

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 64}}{2 \cdot 1}$

Step 4.1.2.2

Multiply

- 4

$- 4$ by

- 64

$- 64$ .

x = \frac{0 \pm \sqrt{0 + 256}}{2 \cdot 1}

$x = \frac{0 \pm \sqrt{0 + 256}}{2 \cdot 1}$

x = \frac{0 \pm \sqrt{0 + 256}}{2 \cdot 1}

$x = \frac{0 \pm \sqrt{0 + 256}}{2 \cdot 1}$

Step 4.1.3

Add

0

$0$ and

256

$256$ .

x = \frac{0 \pm \sqrt{256}}{2 \cdot 1}

$x = \frac{0 \pm \sqrt{256}}{2 \cdot 1}$

Step 4.1.4

Rewrite

256

$256$ as

16^{2}

$16^{2}$ .

x = \frac{0 \pm \sqrt{16^{2}}}{2 \cdot 1}

$x = \frac{0 \pm \sqrt{16^{2}}}{2 \cdot 1}$

Step 4.1.5

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

x = \frac{0 \pm 16}{2 \cdot 1}

$x = \frac{0 \pm 16}{2 \cdot 1}$

x = \frac{0 \pm 16}{2 \cdot 1}

$x = \frac{0 \pm 16}{2 \cdot 1}$

Step 4.2

Multiply

2

$2$ by

1

$1$ .

x = \frac{0 \pm 16}{2}

$x = \frac{0 \pm 16}{2}$

Step 4.3

Simplify

\frac{0 \pm 16}{2}

$\frac{0 \pm 16}{2}$ .

x = \pm 8

$x = \pm 8$

x = \pm 8

$x = \pm 8$

Step 5

The final answer is the combination of both solutions.

x = 8, - 8

$x = 8, - 8$