Solve Using the Square Root Property 5x^2=-8x

$5 x^{2} = - 8 x$

Step 1

Add $8 x$ to both sides of the equation.

$5 x^{2} + 8 x = 0$

Step 2

Factor $x$ out of $5 x^{2} + 8 x$ .

Factor $x$ out of $5 x^{2}$ .

$x (5 x) + 8 x = 0$

Factor $x$ out of $8 x$ .

$x (5 x) + x \cdot 8 = 0$

Factor $x$ out of $x (5 x) + x \cdot 8$ .

$x (5 x + 8) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$5 x + 8 = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $5 x + 8$ equal to $0$ and solve for $x$ .

Set $5 x + 8$ equal to $0$ .

$5 x + 8 = 0$

Solve $5 x + 8 = 0$ for $x$ .

Subtract $8$ from both sides of the equation.

$5 x = - 8$

Divide each term in $5 x = - 8$ by $5$ and simplify.

Divide each term in $5 x = - 8$ by $5$ .

$\frac{5 x}{5} = \frac{- 8}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 8}{5}$

Divide $x$ by $1$ .

$x = \frac{- 8}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8}{5}$

Step 6

The final solution is all the values that make $x (5 x + 8) = 0$ true.

$x = 0, - \frac{8}{5}$