Solve Using the Square Root Property 36x^2=100

$36 x^{2} = 100$

Step 1

Divide each term in $36 x^{2} = 100$ by $36$ and simplify.

Divide each term in $36 x^{2} = 100$ by $36$ .

$\frac{36 x^{2}}{36} = \frac{100}{36}$

Simplify the left side.

Cancel the common factor of $36$ .

Cancel the common factor.

$\frac{36 x^{2}}{36} = \frac{100}{36}$

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

$x^{2} = \frac{100}{36}$

Simplify the right side.

Cancel the common factor of $100$ and $36$ .

Factor $4$ out of $100$ .

$x^{2} = \frac{4 (25)}{36}$

Cancel the common factors.

Factor $4$ out of $36$ .

$x^{2} = \frac{4 \cdot 25}{4 \cdot 9}$

Cancel the common factor.

$x^{2} = \frac{4 \cdot 25}{4 \cdot 9}$

Rewrite the expression.

$x^{2} = \frac{25}{9}$

Step 2

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

$x = \pm \sqrt{\frac{25}{9}}$

Step 3

Simplify $\pm \sqrt{\frac{25}{9}}$ .

Rewrite $\sqrt{\frac{25}{9}}$ as $\frac{\sqrt{25}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{25}}{\sqrt{9}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{5^{2}}}{\sqrt{9}}$

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

$x = \pm \frac{5}{\sqrt{9}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

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

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

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

Step 4

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.

$x = \frac{5}{3}$

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

$x = - \frac{5}{3}$

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

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

Solve Using the Square Root Property 36x^2=100

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