Solve Using the Quadratic Formula 0.7x^2-4.2x-0.7=0

$0.7 x^{2} - 4.2 x - 0.7 = 0$

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 $a = 0.7$ , $b = - 4.2$ , and $c = - 0.7$ into the quadratic formula and solve for $x$ .

$\frac{4.2 \pm \sqrt{{(- 4.2)}^{2} - 4 \cdot (0.7 \cdot - 0.7)}}{2 \cdot 0.7}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 4.2$ to the power of $2$ .

$x = \frac{4.2 \pm \sqrt{17.64 - 4 \cdot 0.7 \cdot - 0.7}}{2 \cdot 0.7}$

Multiply $- 4 \cdot 0.7 \cdot - 0.7$ .

Multiply $- 4$ by $0.7$ .

$x = \frac{4.2 \pm \sqrt{17.64 - 2.8 \cdot - 0.7}}{2 \cdot 0.7}$

Multiply $- 2.8$ by $- 0.7$ .

$x = \frac{4.2 \pm \sqrt{17.64 + 1.96}}{2 \cdot 0.7}$

Add $17.64$ and $1.96$ .

$x = \frac{4.2 \pm \sqrt{19.6}}{2 \cdot 0.7}$

Multiply $2$ by $0.7$ .

$x = \frac{4.2 \pm \sqrt{19.6}}{1.4}$

Simplify $\frac{4.2 \pm \sqrt{19.6}}{1.4}$ .

$x = \frac{21 \pm 5 \sqrt{19.6}}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{21 \pm 5 \sqrt{19.6}}{7}$

Decimal Form:

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