Algebra Examples

x^{2} = 28

$x^{2} = 28$

Step 1

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

x = \pm \sqrt{28}

$x = \pm \sqrt{28}$

Step 2

Simplify

\pm \sqrt{28}

$\pm \sqrt{28}$ .

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Step 2.1

Rewrite

28

$28$ as

2^{2} \cdot 7

$2^{2} \cdot 7$ .

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Step 2.1.1

Factor

4

$4$ out of

28

$28$ .

x = \pm \sqrt{4 (7)}

$x = \pm \sqrt{4 (7)}$

Step 2.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

x = \pm \sqrt{2^{2} \cdot 7}

$x = \pm \sqrt{2^{2} \cdot 7}$

x = \pm \sqrt{2^{2} \cdot 7}

$x = \pm \sqrt{2^{2} \cdot 7}$

Step 2.2

Pull terms out from under the radical.

x = \pm 2 \sqrt{7}

$x = \pm 2 \sqrt{7}$

x = \pm 2 \sqrt{7}

$x = \pm 2 \sqrt{7}$

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 \sqrt{7}

$x = 2 \sqrt{7}$

Step 3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - 2 \sqrt{7}

$x = - 2 \sqrt{7}$

Step 3.3

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

x = 2 \sqrt{7}, - 2 \sqrt{7}

$x = 2 \sqrt{7}, - 2 \sqrt{7}$

x = 2 \sqrt{7}, - 2 \sqrt{7}

$x = 2 \sqrt{7}, - 2 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = 2 \sqrt{7}, - 2 \sqrt{7}

$x = 2 \sqrt{7}, - 2 \sqrt{7}$

Decimal Form:

x = 5.29150262 \dots, - 5.29150262 \dots

$x = 5.29150262 \dots, - 5.29150262 \dots$

x^{2} = 28

$x^{2} = 28$

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