Solve Using the Square Root Property 3x^2-51=0

$3 x^{2} - 51 = 0$

Step 1

Add $51$ to both sides of the equation.

$3 x^{2} = 51$

Step 2

Divide each term in $3 x^{2} = 51$ by $3$ and simplify.

Divide each term in $3 x^{2} = 51$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{51}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{51}{3}$

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

$x^{2} = \frac{51}{3}$

Simplify the right side.

Divide $51$ by $3$ .

$x^{2} = 17$

Step 3

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

$x = \pm \sqrt{17}$

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.

$x = \sqrt{17}$

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

$x = - \sqrt{17}$

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

$x = \sqrt{17}, - \sqrt{17}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{17}, - \sqrt{17}$

Decimal Form:

$x = 4.12310562 \dots, - 4.12310562 \dots$