Solve for x 36x^2-25=0

$36 x^{2} - 25 = 0$

Step 1

Add $25$ to both sides of the equation.

$36 x^{2} = 25$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $36$ .

Cancel the common factor.

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

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

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

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

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

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

Simplify the numerator.

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

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

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

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

Simplify the denominator.

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

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

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.

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

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

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

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

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:

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