Solve Using the Square Root Property 3x^2+4=166

$3 x^{2} + 4 = 166$

Step 1

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

Subtract $4$ from both sides of the equation.

$3 x^{2} = 166 - 4$

Subtract $4$ from $166$ .

$3 x^{2} = 162$

Step 2

Divide each term in $3 x^{2} = 162$ by $3$ and simplify.

Divide each term in $3 x^{2} = 162$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{162}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{162}{3}$

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

$x^{2} = \frac{162}{3}$

Simplify the right side.

Divide $162$ by $3$ .

$x^{2} = 54$

Step 3

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

$x = \pm \sqrt{54}$

Step 4

Simplify $\pm \sqrt{54}$ .

Rewrite $54$ as $3^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$x = \pm \sqrt{9 (6)}$

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

$x = \pm \sqrt{3^{2} \cdot 6}$

Pull terms out from under the radical.

$x = \pm 3 \sqrt{6}$

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.

$x = 3 \sqrt{6}$

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

$x = - 3 \sqrt{6}$

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

$x = 3 \sqrt{6}, - 3 \sqrt{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{6}, - 3 \sqrt{6}$

Decimal Form:

$x = 7.34846922 \dots, - 7.34846922 \dots$

Solve Using the Square Root Property 3x^2+4=166

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