Algebra Examples

{(x - 2)}^{2} = 16

${(x - 2)}^{2} = 16$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

x - 2 = \pm \sqrt{16}

$x - 2 = \pm \sqrt{16}$

Step 2

Simplify

\pm \sqrt{16}

$\pm \sqrt{16}$ .

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Step 2.1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

x - 2 = \pm \sqrt{4^{2}}

$x - 2 = \pm \sqrt{4^{2}}$

Step 2.2

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

x - 2 = \pm 4

$x - 2 = \pm 4$

x - 2 = \pm 4

$x - 2 = \pm 4$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

x - 2 = 4

$x - 2 = 4$

Step 3.2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 3.2.1

Add

2

$2$ to both sides of the equation.

x = 4 + 2

$x = 4 + 2$

Step 3.2.2

Add

4

$4$ and

2

$2$ .

x = 6

$x = 6$

x = 6

$x = 6$

Step 3.3

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x - 2 = - 4

$x - 2 = - 4$

Step 3.4

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 3.4.1

Add

2

$2$ to both sides of the equation.

x = - 4 + 2

$x = - 4 + 2$

Step 3.4.2

Add

- 4

$- 4$ and

2

$2$ .

x = - 2

$x = - 2$

x = - 2

$x = - 2$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

x = 6, - 2

$x = 6, - 2$

x = 6, - 2

$x = 6, - 2$