Solve Using the Quadratic Formula 0.2x^2=0.8x+0.2

$0.2 x^{2} = 0.8 x + 0.2$

Step 1

Move all the expressions to the left side of the equation.

Subtract $0.8 x$ from both sides of the equation.

$0.2 x^{2} - 0.8 x = 0.2$

Subtract $0.2$ from both sides of the equation.

$0.2 x^{2} - 0.8 x - 0.2 = 0$

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 $a = 0.2$ , $b = - 0.8$ , and $c = - 0.2$ into the quadratic formula and solve for $x$ .

$\frac{0.8 \pm \sqrt{{(- 0.8)}^{2} - 4 \cdot (0.2 \cdot - 0.2)}}{2 \cdot 0.2}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 0.8$ to the power of $2$ .

$x = \frac{0.8 \pm \sqrt{0.64 - 4 \cdot 0.2 \cdot - 0.2}}{2 \cdot 0.2}$

Multiply $- 4 \cdot 0.2 \cdot - 0.2$ .

Multiply $- 4$ by $0.2$ .

$x = \frac{0.8 \pm \sqrt{0.64 - 0.8 \cdot - 0.2}}{2 \cdot 0.2}$

Multiply $- 0.8$ by $- 0.2$ .

$x = \frac{0.8 \pm \sqrt{0.64 + 0.16}}{2 \cdot 0.2}$

Add $0.64$ and $0.16$ .

$x = \frac{0.8 \pm \sqrt{0.8}}{2 \cdot 0.2}$

Multiply $2$ by $0.2$ .

$x = \frac{0.8 \pm \sqrt{0.8}}{0.4}$

Simplify $\frac{0.8 \pm \sqrt{0.8}}{0.4}$ .

$x = \frac{4 \pm 5 \sqrt{0.8}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4 \pm 5 \sqrt{0.8}}{2}$

Decimal Form:

$x = 4.23606797 \dots, - 0.23606797 \dots$