Solve Using the Square Root Property 108x^2=147

$108 x^{2} = 147$

Step 1

Divide each term in $108 x^{2} = 147$ by $108$ and simplify.

Divide each term in $108 x^{2} = 147$ by $108$ .

$\frac{108 x^{2}}{108} = \frac{147}{108}$

Simplify the left side.

Cancel the common factor of $108$ .

Cancel the common factor.

$\frac{108 x^{2}}{108} = \frac{147}{108}$

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

$x^{2} = \frac{147}{108}$

Simplify the right side.

Cancel the common factor of $147$ and $108$ .

Factor $3$ out of $147$ .

$x^{2} = \frac{3 (49)}{108}$

Cancel the common factors.

Factor $3$ out of $108$ .

$x^{2} = \frac{3 \cdot 49}{3 \cdot 36}$

Cancel the common factor.

$x^{2} = \frac{3 \cdot 49}{3 \cdot 36}$

Rewrite the expression.

$x^{2} = \frac{49}{36}$

Step 2

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

$x = \pm \sqrt{\frac{49}{36}}$

Step 3

Simplify $\pm \sqrt{\frac{49}{36}}$ .

Rewrite $\sqrt{\frac{49}{36}}$ as $\frac{\sqrt{49}}{\sqrt{36}}$ .

$x = \pm \frac{\sqrt{49}}{\sqrt{36}}$

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$x = \pm \frac{\sqrt{7^{2}}}{\sqrt{36}}$

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

$x = \pm \frac{7}{\sqrt{36}}$

Simplify the denominator.

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

$x = \pm \frac{7}{\sqrt{6^{2}}}$

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

$x = \pm \frac{7}{6}$

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.

$x = \frac{7}{6}$

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

$x = - \frac{7}{6}$

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

$x = \frac{7}{6}, - \frac{7}{6}$

Solve Using the Square Root Property 108x^2=147

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