Solve Using the Quadratic Formula 8x^2+21=-59x

$8 x^{2} + 21 = - 59 x$

Step 1

Add $59 x$ to both sides of the equation.

$8 x^{2} + 21 + 59 x = 0$

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 $a = 8$ , $b = 59$ , and $c = 21$ into the quadratic formula and solve for $x$ .

$\frac{- 59 \pm \sqrt{59^{2} - 4 \cdot (8 \cdot 21)}}{2 \cdot 8}$

Step 4

Simplify.

Simplify the numerator.

Raise $59$ to the power of $2$ .

$x = \frac{- 59 \pm \sqrt{3481 - 4 \cdot 8 \cdot 21}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot 21$ .

Multiply $- 4$ by $8$ .

$x = \frac{- 59 \pm \sqrt{3481 - 32 \cdot 21}}{2 \cdot 8}$

Multiply $- 32$ by $21$ .

$x = \frac{- 59 \pm \sqrt{3481 - 672}}{2 \cdot 8}$

Subtract $672$ from $3481$ .

$x = \frac{- 59 \pm \sqrt{2809}}{2 \cdot 8}$

Rewrite $2809$ as $53^{2}$ .

$x = \frac{- 59 \pm \sqrt{53^{2}}}{2 \cdot 8}$

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

$x = \frac{- 59 \pm 53}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{- 59 \pm 53}{16}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{3}{8}, - 7$