Algebra Examples

x^{2} = 45

$x^{2} = 45$

Step 1

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

x = \pm \sqrt{45}

$x = \pm \sqrt{45}$

Step 2

Simplify

\pm \sqrt{45}

$\pm \sqrt{45}$ .

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Step 2.1

Rewrite

45

$45$ as

3^{2} \cdot 5

$3^{2} \cdot 5$ .

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Step 2.1.1

Factor

9

$9$ out of

45

$45$ .

x = \pm \sqrt{9 (5)}

$x = \pm \sqrt{9 (5)}$

Step 2.1.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

x = \pm \sqrt{3^{2} \cdot 5}

$x = \pm \sqrt{3^{2} \cdot 5}$

x = \pm \sqrt{3^{2} \cdot 5}

$x = \pm \sqrt{3^{2} \cdot 5}$

Step 2.2

Pull terms out from under the radical.

x = \pm 3 \sqrt{5}

$x = \pm 3 \sqrt{5}$

x = \pm 3 \sqrt{5}

$x = \pm 3 \sqrt{5}$

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 = 3 \sqrt{5}

$x = 3 \sqrt{5}$

Step 3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - 3 \sqrt{5}

$x = - 3 \sqrt{5}$

Step 3.3

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

x = 3 \sqrt{5}, - 3 \sqrt{5}

$x = 3 \sqrt{5}, - 3 \sqrt{5}$

x = 3 \sqrt{5}, - 3 \sqrt{5}

$x = 3 \sqrt{5}, - 3 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = 3 \sqrt{5}, - 3 \sqrt{5}

$x = 3 \sqrt{5}, - 3 \sqrt{5}$

Decimal Form:

x = 6.70820393 \dots, - 6.70820393 \dots

$x = 6.70820393 \dots, - 6.70820393 \dots$

x^{2} = 45

$x^{2} = 45$

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