Find the Roots (Zeros) 16x^2+16=0

$16 x^{2} + 16 = 0$

Step 1

Subtract $16$ from both sides of the equation.

$16 x^{2} = - 16$

Step 2

Divide each term in $16 x^{2} = - 16$ by $16$ and simplify.

Divide each term in $16 x^{2} = - 16$ by $16$ .

$\frac{16 x^{2}}{16} = \frac{- 16}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x^{2}}{16} = \frac{- 16}{16}$

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

$x^{2} = \frac{- 16}{16}$

Simplify the right side.

Divide $- 16$ by $16$ .

$x^{2} = - 1$

Step 3

Take the square 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.

$x = i, - i$

Step 6