Solve Using the Square Root Property 7x^2=49

$7 x^{2} = 49$

Step 1

Divide each term in $7 x^{2} = 49$ by $7$ and simplify.

Divide each term in $7 x^{2} = 49$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{49}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{49}{7}$

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

$x^{2} = \frac{49}{7}$

Simplify the right side.

Divide $49$ by $7$ .

$x^{2} = 7$

Step 2

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

$x = \pm \sqrt{7}$

Step 3

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.

$x = \sqrt{7}$

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

$x = - \sqrt{7}$

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

$x = \sqrt{7}, - \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{7}, - \sqrt{7}$

Decimal Form:

$x = 2.64575131 \dots, - 2.64575131 \dots$