Solve by Factoring 9x^2+21-8=0

$9 x^{2} + 21 - 8 = 0$

Step 1

Subtract $8$ from $21$ .

$9 x^{2} + 13 = 0$

Step 2

Subtract $13$ from both sides of the equation.

$9 x^{2} = - 13$

Step 3

Divide each term in $9 x^{2} = - 13$ by $9$ and simplify.

Divide each term in $9 x^{2} = - 13$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{- 13}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{- 13}{9}$

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

$x^{2} = \frac{- 13}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$x^{2} = - \frac{13}{9}$

Step 4

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

$x = \pm \sqrt{- \frac{13}{9}}$

Step 5

Simplify $\pm \sqrt{- \frac{13}{9}}$ .

Rewrite $- \frac{13}{9}$ as ${(\frac{i}{3})}^{2} \cdot 13$ .

Rewrite $- 1$ as $i^{2}$ .

$x = \pm \sqrt{i^{2} \frac{13}{9}}$

Factor the perfect power $1^{2}$ out of $13$ .

$x = \pm \sqrt{i^{2} \frac{1^{2} \cdot 13}{9}}$

Factor the perfect power $3^{2}$ out of $9$ .

$x = \pm \sqrt{i^{2} \frac{1^{2} \cdot 13}{3^{2} \cdot 1}}$

Rearrange the fraction $\frac{1^{2} \cdot 13}{3^{2} \cdot 1}$ .

$x = \pm \sqrt{i^{2} ({(\frac{1}{3})}^{2} \cdot 13)}$

Rewrite $i^{2} {(\frac{1}{3})}^{2}$ as ${(\frac{i}{3})}^{2}$ .

$x = \pm \sqrt{{(\frac{i}{3})}^{2} \cdot 13}$

Pull terms out from under the radical.

$x = \pm \frac{i}{3} \sqrt{13}$

Combine $\frac{i}{3}$ and $\sqrt{13}$ .

$x = \pm \frac{i \sqrt{13}}{3}$

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.

$x = \frac{i \sqrt{13}}{3}$

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

$x = - \frac{i \sqrt{13}}{3}$

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

$x = \frac{i \sqrt{13}}{3}, - \frac{i \sqrt{13}}{3}$

Solve by Factoring 9x^2+21-8=0

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