Solve Using the Square Root Property 100x^2=64

$100 x^{2} = 64$

Step 1

Divide each term in $100 x^{2} = 64$ by $100$ and simplify.

Divide each term in $100 x^{2} = 64$ by $100$ .

$\frac{100 x^{2}}{100} = \frac{64}{100}$

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$\frac{100 x^{2}}{100} = \frac{64}{100}$

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

$x^{2} = \frac{64}{100}$

Simplify the right side.

Cancel the common factor of $64$ and $100$ .

Factor $4$ out of $64$ .

$x^{2} = \frac{4 (16)}{100}$

Cancel the common factors.

Factor $4$ out of $100$ .

$x^{2} = \frac{4 \cdot 16}{4 \cdot 25}$

Cancel the common factor.

$x^{2} = \frac{4 \cdot 16}{4 \cdot 25}$

Rewrite the expression.

$x^{2} = \frac{16}{25}$

Step 2

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

$x = \pm \sqrt{\frac{16}{25}}$

Step 3

Simplify $\pm \sqrt{\frac{16}{25}}$ .

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$x = \pm \frac{\sqrt{16}}{\sqrt{25}}$

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$x = \pm \frac{\sqrt{4^{2}}}{\sqrt{25}}$

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

$x = \pm \frac{4}{\sqrt{25}}$

Simplify the denominator.

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

$x = \pm \frac{4}{\sqrt{5^{2}}}$

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

$x = \pm \frac{4}{5}$

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.

$x = \frac{4}{5}$

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

$x = - \frac{4}{5}$

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

$x = \frac{4}{5}, - \frac{4}{5}$

Solve Using the Square Root Property 100x^2=64

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