Solve Using the Quadratic Formula 5d^2-22d+8=0

$5 d^{2} - 22 d + 8 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 5$ , $b = - 22$ , and $c = 8$ into the quadratic formula and solve for $d$ .

$\frac{22 \pm \sqrt{{(- 22)}^{2} - 4 \cdot (5 \cdot 8)}}{2 \cdot 5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 22$ to the power of $2$ .

$d = \frac{22 \pm \sqrt{484 - 4 \cdot 5 \cdot 8}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot 8$ .

Multiply $- 4$ by $5$ .

$d = \frac{22 \pm \sqrt{484 - 20 \cdot 8}}{2 \cdot 5}$

Multiply $- 20$ by $8$ .

$d = \frac{22 \pm \sqrt{484 - 160}}{2 \cdot 5}$

Subtract $160$ from $484$ .

$d = \frac{22 \pm \sqrt{324}}{2 \cdot 5}$

Rewrite $324$ as $18^{2}$ .

$d = \frac{22 \pm \sqrt{18^{2}}}{2 \cdot 5}$

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

$d = \frac{22 \pm 18}{2 \cdot 5}$

Multiply $2$ by $5$ .

$d = \frac{22 \pm 18}{10}$

Simplify $\frac{22 \pm 18}{10}$ .

$d = \frac{11 \pm 9}{5}$

Step 4

The final answer is the combination of both solutions.

$d = 4, \frac{2}{5}$