Solve Using the Square Root Property 9x^2+100=0

$9 x^{2} + 100 = 0$

Step 1

Subtract $100$ from both sides of the equation.

$9 x^{2} = - 100$

Step 2

Divide each term in $9 x^{2} = - 100$ by $9$ and simplify.

Divide each term in $9 x^{2} = - 100$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{- 100}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{- 100}{9}$

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

$x^{2} = \frac{- 100}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$x^{2} = - \frac{100}{9}$

Step 3

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

$x = \pm \sqrt{- \frac{100}{9}}$

Step 4

Simplify $\pm \sqrt{- \frac{100}{9}}$ .

Rewrite $- \frac{100}{9}$ as ${(\frac{10 i}{3})}^{2}$ .

$x = \pm \sqrt{{(\frac{10 i}{3})}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{10 i}{3}$

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.

$x = \frac{10 i}{3}$

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

$x = - \frac{10 i}{3}$

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

$x = \frac{10 i}{3}, - \frac{10 i}{3}$