Solve for x 4x^2+4=0

$4 x^{2} + 4 = 0$

Step 1

Subtract $4$ from both sides of the equation.

$4 x^{2} = - 4$

Step 2

Divide each term in $4 x^{2} = - 4$ by $4$ and simplify.

Divide each term in $4 x^{2} = - 4$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{- 4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{- 4}{4}$

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

$x^{2} = \frac{- 4}{4}$

Simplify the right side.

Divide $- 4$ by $4$ .

$x^{2} = - 1$

Step 3

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

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

Step 4

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

$x = \pm i$

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.

$x = i$

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.

$x = i, - i$