Find All Complex Solutions 3.2x^2-2x+1.3=0

$3.2 x^{2} - 2 x + 1.3 = 0$

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 $a = 3.2$ , $b = - 2$ , and $c = 1.3$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (3.2 \cdot 1.3)}}{2 \cdot 3.2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 3.2 \cdot 1.3}}{2 \cdot 3.2}$

Multiply $- 4 \cdot 3.2 \cdot 1.3$ .

Multiply $- 4$ by $3.2$ .

$x = \frac{2 \pm \sqrt{4 - 12.8 \cdot 1.3}}{2 \cdot 3.2}$

Multiply $- 12.8$ by $1.3$ .

$x = \frac{2 \pm \sqrt{4 - 16.64}}{2 \cdot 3.2}$

Subtract $16.64$ from $4$ .

$x = \frac{2 \pm \sqrt{- 12.64}}{2 \cdot 3.2}$

Rewrite $- 12.64$ as $- 1 (12.64)$ .

$x = \frac{2 \pm \sqrt{- 1 \cdot 12.64}}{2 \cdot 3.2}$

Rewrite $\sqrt{- 1 (12.64)}$ as $\sqrt{- 1} \cdot \sqrt{12.64}$ .

$x = \frac{2 \pm \sqrt{- 1} \cdot \sqrt{12.64}}{2 \cdot 3.2}$

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

$x = \frac{2 \pm i \sqrt{12.64}}{2 \cdot 3.2}$

Multiply $2$ by $3.2$ .

$x = \frac{2 \pm i \sqrt{12.64}}{6.4}$

Simplify $\frac{2 \pm i \sqrt{12.64}}{6.4}$ .

$x = \frac{10 \pm 5 i \sqrt{12.64}}{32}$