Solve by Factoring 64x^2=-49

$64 x^{2} = - 49$

Step 1

Add $49$ to both sides of the equation.

$64 x^{2} + 49 = 0$

Step 2

Subtract $49$ from both sides of the equation.

$64 x^{2} = - 49$

Step 3

Divide each term in $64 x^{2} = - 49$ by $64$ and simplify.

Divide each term in $64 x^{2} = - 49$ by $64$ .

$\frac{64 x^{2}}{64} = \frac{- 49}{64}$

Simplify the left side.

Cancel the common factor of $64$ .

Cancel the common factor.

$\frac{64 x^{2}}{64} = \frac{- 49}{64}$

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

$x^{2} = \frac{- 49}{64}$

Simplify the right side.

Move the negative in front of the fraction.

$x^{2} = - \frac{49}{64}$

Step 4

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

$x = \pm \sqrt{- \frac{49}{64}}$

Step 5

Simplify $\pm \sqrt{- \frac{49}{64}}$ .

Rewrite $- \frac{49}{64}$ as ${(\frac{7 i}{8})}^{2}$ .

$x = \pm \sqrt{{(\frac{7 i}{8})}^{2}}$

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

$x = \pm \frac{7 i}{8}$

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.

$x = \frac{7 i}{8}$

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

$x = - \frac{7 i}{8}$

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

$x = \frac{7 i}{8}, - \frac{7 i}{8}$