Solve Using the Quadratic Formula 0.6x^2-1.2x-0.6=0

$0.6 x^{2} - 1.2 x - 0.6 = 0$

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 $a = 0.6$ , $b = - 1.2$ , and $c = - 0.6$ into the quadratic formula and solve for $x$ .

$\frac{1.2 \pm \sqrt{{(- 1.2)}^{2} - 4 \cdot (0.6 \cdot - 0.6)}}{2 \cdot 0.6}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 1.2$ to the power of $2$ .

$x = \frac{1.2 \pm \sqrt{1.44 - 4 \cdot 0.6 \cdot - 0.6}}{2 \cdot 0.6}$

Multiply $- 4 \cdot 0.6 \cdot - 0.6$ .

Multiply $- 4$ by $0.6$ .

$x = \frac{1.2 \pm \sqrt{1.44 - 2.4 \cdot - 0.6}}{2 \cdot 0.6}$

Multiply $- 2.4$ by $- 0.6$ .

$x = \frac{1.2 \pm \sqrt{1.44 + 1.44}}{2 \cdot 0.6}$

Add $1.44$ and $1.44$ .

$x = \frac{1.2 \pm \sqrt{2.88}}{2 \cdot 0.6}$

Multiply $2$ by $0.6$ .

$x = \frac{1.2 \pm \sqrt{2.88}}{1.2}$

Simplify $\frac{1.2 \pm \sqrt{2.88}}{1.2}$ .

$x = \frac{6 \pm 5 \sqrt{2.88}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{6 \pm 5 \sqrt{2.88}}{6}$

Decimal Form:

$x = 2.41421356 \dots, - 0.41421356 \dots$