Algebra Examples

{(x - 2)}^{2} = 64

${(x - 2)}^{2} = 64$

Step 1

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

x - 2 = \pm \sqrt{64}

$x - 2 = \pm \sqrt{64}$

Step 2

Simplify

\pm \sqrt{64}

$\pm \sqrt{64}$ .

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Step 2.1

Rewrite

64

$64$ as

8^{2}

$8^{2}$ .

x - 2 = \pm \sqrt{8^{2}}

$x - 2 = \pm \sqrt{8^{2}}$

Step 2.2

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

x - 2 = \pm 8

$x - 2 = \pm 8$

x - 2 = \pm 8

$x - 2 = \pm 8$

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 = 8

$x - 2 = 8$

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 = 8 + 2

$x = 8 + 2$

Step 3.2.2

Add

8

$8$ and

2

$2$ .

x = 10

$x = 10$

x = 10

$x = 10$

Step 3.3

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x - 2 = - 8

$x - 2 = - 8$

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 = - 8 + 2

$x = - 8 + 2$

Step 3.4.2

Add

- 8

$- 8$ and

2

$2$ .

x = - 6

$x = - 6$

x = - 6

$x = - 6$

Step 3.5

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

x = 10, - 6

$x = 10, - 6$

x = 10, - 6

$x = 10, - 6$

{(x - 2)}^{2} = 64

${(x - 2)}^{2} = 64$

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