Solve Using the Quadratic Formula 0.2x-0.4x^2=-2

$0.2 x - 0.4 x^{2} = - 2$

Step 1

Add $2$ to both sides of the equation.

$0.2 x - 0.4 x^{2} + 2 = 0$

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 $a = - 0.4$ , $b = 0.2$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{- 0.2 \pm \sqrt{{0.2}^{2} - 4 \cdot (- 0.4 \cdot 2)}}{2 \cdot - 0.4}$

Step 4

Simplify.

Simplify the numerator.

Raise $0.2$ to the power of $2$ .

$x = \frac{- 0.2 \pm \sqrt{0.04 - 4 \cdot - 0.4 \cdot 2}}{2 \cdot - 0.4}$

Multiply $- 4 \cdot - 0.4 \cdot 2$ .

Multiply $- 4$ by $- 0.4$ .

$x = \frac{- 0.2 \pm \sqrt{0.04 + 1.6 \cdot 2}}{2 \cdot - 0.4}$

Multiply $1.6$ by $2$ .

$x = \frac{- 0.2 \pm \sqrt{0.04 + 3.2}}{2 \cdot - 0.4}$

Add $0.04$ and $3.2$ .

$x = \frac{- 0.2 \pm \sqrt{3.24}}{2 \cdot - 0.4}$

Rewrite $3.24$ as ${1.8}^{2}$ .

$x = \frac{- 0.2 \pm \sqrt{{1.8}^{2}}}{2 \cdot - 0.4}$

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

$x = \frac{- 0.2 \pm 1.8}{2 \cdot - 0.4}$

Multiply $2$ by $- 0.4$ .

$x = \frac{- 0.2 \pm 1.8}{- 0.8}$

Simplify $\frac{- 0.2 \pm 1.8}{- 0.8}$ .

$x = \frac{1 \pm 9}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{2}, - 2$