Pre-Algebra Examples

$49 x^{2} = 36$

Step 1

Divide each term in $49 x^{2} = 36$ by $49$ and simplify.

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Step 1.1

Divide each term in $49 x^{2} = 36$ by $49$ .

$\frac{49 x^{2}}{49} = \frac{36}{49}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $49$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{49 x^{2}}{49} = \frac{36}{49}$

Step 1.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{36}{49}$

Step 2

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

$x = \pm \sqrt{\frac{36}{49}}$

Step 3

Simplify $\pm \sqrt{\frac{36}{49}}$ .

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Step 3.1

Rewrite $\sqrt{\frac{36}{49}}$ as $\frac{\sqrt{36}}{\sqrt{49}}$ .

$x = \pm \frac{\sqrt{36}}{\sqrt{49}}$

Step 3.2

Simplify the numerator.

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Step 3.2.1

Rewrite $36$ as $6^{2}$ .

$x = \pm \frac{\sqrt{6^{2}}}{\sqrt{49}}$

Step 3.2.2

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

$x = \pm \frac{6}{\sqrt{49}}$

Step 3.3

Simplify the denominator.

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Step 3.3.1

Rewrite $49$ as $7^{2}$ .

$x = \pm \frac{6}{\sqrt{7^{2}}}$

Step 3.3.2

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

$x = \pm \frac{6}{7}$

Step 4

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

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$x = \frac{6}{7}$

Step 4.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \frac{6}{7}$

Step 4.3

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

$x = \frac{6}{7}, - \frac{6}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6}{7}, - \frac{6}{7}$

Decimal Form:

$x = 0.\overline{857142}, - 0.\overline{857142}$