Solve Using the Quadratic Formula 0.5x^2-3x-0.5=0

$0.5 x^{2} - 3 x - 0.5 = 0$

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 $a = 0.5$ , $b = - 3$ , and $c = - 0.5$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (0.5 \cdot - 0.5)}}{2 \cdot 0.5}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 0.5 \cdot - 0.5}}{2 \cdot 0.5}$

Multiply $- 4 \cdot 0.5 \cdot - 0.5$ .

Multiply $- 4$ by $0.5$ .

$x = \frac{3 \pm \sqrt{9 - 2 \cdot - 0.5}}{2 \cdot 0.5}$

Multiply $- 2$ by $- 0.5$ .

$x = \frac{3 \pm \sqrt{9 + 1}}{2 \cdot 0.5}$

Add $9$ and $1$ .

$x = \frac{3 \pm \sqrt{10}}{2 \cdot 0.5}$

Multiply $2$ by $0.5$ .

$x = \frac{3 \pm \sqrt{10}}{1}$

Divide $3 \pm \sqrt{10}$ by $1$ .

$x = 3 \pm \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 3 \pm \sqrt{10}$

Decimal Form:

$x = 6.16227766 \dots, - 0.16227766 \dots$