Solve Using the Square Root Property 5x^2-15=45

$5 x^{2} - 15 = 45$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $15$ to both sides of the equation.

$5 x^{2} = 45 + 15$

Add $45$ and $15$ .

$5 x^{2} = 60$

Step 2

Divide each term in $5 x^{2} = 60$ by $5$ and simplify.

Divide each term in $5 x^{2} = 60$ by $5$ .

$\frac{5 x^{2}}{5} = \frac{60}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x^{2}}{5} = \frac{60}{5}$

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

$x^{2} = \frac{60}{5}$

Simplify the right side.

Divide $60$ by $5$ .

$x^{2} = 12$

Step 3

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

$x = \pm \sqrt{12}$

Step 4

Simplify $\pm \sqrt{12}$ .

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$x = \pm \sqrt{4 (3)}$

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

$x = \pm \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm 2 \sqrt{3}$

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.

$x = 2 \sqrt{3}$

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

$x = - 2 \sqrt{3}$

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

$x = 2 \sqrt{3}, - 2 \sqrt{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{3}, - 2 \sqrt{3}$

Decimal Form:

$x = 3.46410161 \dots, - 3.46410161 \dots$

Solve Using the Square Root Property 5x^2-15=45

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