Solve Using the Square Root Property 49x^2+64=0

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

Step 1

Subtract $64$ from both sides of the equation.

$49 x^{2} = - 64$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

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

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

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

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

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

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

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

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

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.

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

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

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

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

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