Algebra Examples

$13 - 36 x^{2} = - 12$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Subtract $13$ from both sides of the equation.

$- 36 x^{2} = - 12 - 13$

Step 1.2

Subtract $13$ from $- 12$ .

$- 36 x^{2} = - 25$

Step 2

Divide each term in $- 36 x^{2} = - 25$ by $- 36$ and simplify.

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Step 2.1

Divide each term in $- 36 x^{2} = - 25$ by $- 36$ .

$\frac{- 36 x^{2}}{- 36} = \frac{- 25}{- 36}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 36$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 36 x^{2}}{- 36} = \frac{- 25}{- 36}$

Step 2.2.1.2

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

$x^{2} = \frac{- 25}{- 36}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Dividing two negative values results in a positive value.

$x^{2} = \frac{25}{36}$

Step 3

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

$x = \pm \sqrt{\frac{25}{36}}$

Step 4

Simplify $\pm \sqrt{\frac{25}{36}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{25}{36}}$ as $\frac{\sqrt{25}}{\sqrt{36}}$ .

$x = \pm \frac{\sqrt{25}}{\sqrt{36}}$

Step 4.2

Simplify the numerator.

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Step 4.2.1

Rewrite $25$ as $5^{2}$ .

$x = \pm \frac{\sqrt{5^{2}}}{\sqrt{36}}$

Step 4.2.2

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

$x = \pm \frac{5}{\sqrt{36}}$

Step 4.3

Simplify the denominator.

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Step 4.3.1

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

$x = \pm \frac{5}{\sqrt{6^{2}}}$

Step 4.3.2

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

$x = \pm \frac{5}{6}$

Step 5

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

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Step 5.1

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

$x = \frac{5}{6}$

Step 5.2

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

$x = - \frac{5}{6}$

Step 5.3

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

$x = \frac{5}{6}, - \frac{5}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{6}, - \frac{5}{6}$

Decimal Form:

$x = 0.8\overline{3}, - 0.8\overline{3}$