Solve Using the Quadratic Formula 1.6x^2+2x+2.5=0

$1.6 x^{2} + 2 x + 2.5 = 0$

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 $a = 1.6$ , $b = 2$ , and $c = 2.5$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1.6 \cdot 2.5)}}{2 \cdot 1.6}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1.6 \cdot 2.5}}{2 \cdot 1.6}$

Multiply $- 4 \cdot 1.6 \cdot 2.5$ .

Multiply $- 4$ by $1.6$ .

$x = \frac{- 2 \pm \sqrt{4 - 6.4 \cdot 2.5}}{2 \cdot 1.6}$

Multiply $- 6.4$ by $2.5$ .

$x = \frac{- 2 \pm \sqrt{4 - 16}}{2 \cdot 1.6}$

Subtract $16$ from $4$ .

$x = \frac{- 2 \pm \sqrt{- 12}}{2 \cdot 1.6}$

Rewrite $- 12$ as $- 1 (12)$ .

$x = \frac{- 2 \pm \sqrt{- 1 \cdot 12}}{2 \cdot 1.6}$

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$x = \frac{- 2 \pm \sqrt{- 1} \cdot \sqrt{12}}{2 \cdot 1.6}$

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

$x = \frac{- 2 \pm i \sqrt{12}}{2 \cdot 1.6}$

Multiply $2$ by $1.6$ .

$x = \frac{- 2 \pm i \sqrt{12}}{3.2}$

Simplify $\frac{- 2 \pm i \sqrt{12}}{3.2}$ .

$x = \frac{- 10 \pm 5 i \sqrt{12}}{16}$