Solve Using the Square Root Property 100=4x^2

$100 = 4 x^{2}$

Step 1

Rewrite the equation as $4 x^{2} = 100$ .

$4 x^{2} = 100$

Step 2

Divide each term in $4 x^{2} = 100$ by $4$ and simplify.

Divide each term in $4 x^{2} = 100$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{100}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{100}{4}$

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

$x^{2} = \frac{100}{4}$

Simplify the right side.

Divide $100$ by $4$ .

$x^{2} = 25$

Step 3

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

$x = \pm \sqrt{25}$

Step 4

Simplify $\pm \sqrt{25}$ .

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

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

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

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$