Solve by Factoring 5x^2+5=0

$5 x^{2} + 5 = 0$

Step 1

Factor $5$ out of $5 x^{2} + 5$ .

Factor $5$ out of $5 x^{2}$ .

$5 (x^{2}) + 5 = 0$

Factor $5$ out of $5$ .

$5 (x^{2}) + 5 (1) = 0$

Factor $5$ out of $5 (x^{2}) + 5 (1)$ .

$5 (x^{2} + 1) = 0$

Step 2

Divide each term in $5 (x^{2} + 1) = 0$ by $5$ and simplify.

Divide each term in $5 (x^{2} + 1) = 0$ by $5$ .

$\frac{5 (x^{2} + 1)}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (x^{2} + 1)}{5} = \frac{0}{5}$

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

$x^{2} + 1 = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

$x^{2} + 1 = 0$

Step 3

Subtract $1$ from both sides of the equation.

$x^{2} = - 1$

Step 4

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

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

Step 5

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

$x = \pm i$

Step 6

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.

$x = i$

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

$x = - i$

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

$x = i, - i$