Solve Using the Square Root Property 7x^2+46=32

$7 x^{2} + 46 = 32$

Step 1

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

Subtract $46$ from both sides of the equation.

$7 x^{2} = 32 - 46$

Subtract $46$ from $32$ .

$7 x^{2} = - 14$

Step 2

Divide each term in $7 x^{2} = - 14$ by $7$ and simplify.

Divide each term in $7 x^{2} = - 14$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{- 14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x^{2}}{7} = \frac{- 14}{7}$

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

$x^{2} = \frac{- 14}{7}$

Simplify the right side.

Divide $- 14$ by $7$ .

$x^{2} = - 2$

Step 3

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

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

Step 4

Simplify $\pm \sqrt{- 2}$ .

Rewrite $- 2$ as $- 1 (2)$ .

$x = \pm \sqrt{- 1 (2)}$

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{2}$

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

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

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.

$x = i \sqrt{2}$

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

$x = - i \sqrt{2}$

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

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