Solve Using the Quadratic Formula 5x^2=-30x-65

$5 x^{2} = - 30 x - 65$

Step 1

Move all the expressions to the left side of the equation.

Add $30 x$ to both sides of the equation.

$5 x^{2} + 30 x = - 65$

Add $65$ to both sides of the equation.

$5 x^{2} + 30 x + 65 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 5$ , $b = 30$ , and $c = 65$ into the quadratic formula and solve for $x$ .

$\frac{- 30 \pm \sqrt{30^{2} - 4 \cdot (5 \cdot 65)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $30$ to the power of $2$ .

$x = \frac{- 30 \pm \sqrt{900 - 4 \cdot 5 \cdot 65}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 65$ .

Multiply $- 4$ by $5$ .

$x = \frac{- 30 \pm \sqrt{900 - 20 \cdot 65}}{2 \cdot 5}$

Multiply $- 20$ by $65$ .

$x = \frac{- 30 \pm \sqrt{900 - 1300}}{2 \cdot 5}$

Subtract $1300$ from $900$ .

$x = \frac{- 30 \pm \sqrt{- 400}}{2 \cdot 5}$

Rewrite $- 400$ as $- 1 (400)$ .

$x = \frac{- 30 \pm \sqrt{- 1 \cdot 400}}{2 \cdot 5}$

Rewrite $\sqrt{- 1 (400)}$ as $\sqrt{- 1} \cdot \sqrt{400}$ .

$x = \frac{- 30 \pm \sqrt{- 1} \cdot \sqrt{400}}{2 \cdot 5}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{- 30 \pm i \cdot \sqrt{400}}{2 \cdot 5}$

Rewrite $400$ as $20^{2}$ .

$x = \frac{- 30 \pm i \cdot \sqrt{20^{2}}}{2 \cdot 5}$

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

$x = \frac{- 30 \pm i \cdot 20}{2 \cdot 5}$

Move $20$ to the left of $i$ .

$x = \frac{- 30 \pm 20 i}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 30 \pm 20 i}{10}$

Simplify $\frac{- 30 \pm 20 i}{10}$ .

$x = - 3 \pm 2 i$