Solve Using the Square Root Property 7x^2=-21

$7 x^{2} = - 21$

Step 1

Divide each term in $7 x^{2} = - 21$ by $7$ and simplify.

Divide each term in $7 x^{2} = - 21$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{- 21}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{- 21}{7}$

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

$x^{2} = \frac{- 21}{7}$

Simplify the right side.

Divide $- 21$ by $7$ .

$x^{2} = - 3$

Step 2

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

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

Step 3

Simplify $\pm \sqrt{- 3}$ .

Rewrite $- 3$ as $- 1 (3)$ .

$x = \pm \sqrt{- 1 (3)}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{3}$

Rewrite $\sqrt{- 1}$ as $i$ .

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

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.

$x = i \sqrt{3}$

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

$x = - i \sqrt{3}$

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

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