Solve Using the Quadratic Formula 0.7x-0.6x^2=-1

$0.7 x - 0.6 x^{2} = - 1$

Step 1

Add $1$ to both sides of the equation.

$0.7 x - 0.6 x^{2} + 1 = 0$

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 $a = - 0.6$ , $b = 0.7$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 0.7 \pm \sqrt{{0.7}^{2} - 4 \cdot (- 0.6 \cdot 1)}}{2 \cdot - 0.6}$

Step 4

Simplify.

Simplify the numerator.

Raise $0.7$ to the power of $2$ .

$x = \frac{- 0.7 \pm \sqrt{0.49 - 4 \cdot - 0.6 \cdot 1}}{2 \cdot - 0.6}$

Multiply $- 4 \cdot - 0.6 \cdot 1$ .

Multiply $- 4$ by $- 0.6$ .

$x = \frac{- 0.7 \pm \sqrt{0.49 + 2.4 \cdot 1}}{2 \cdot - 0.6}$

Multiply $2.4$ by $1$ .

$x = \frac{- 0.7 \pm \sqrt{0.49 + 2.4}}{2 \cdot - 0.6}$

Add $0.49$ and $2.4$ .

$x = \frac{- 0.7 \pm \sqrt{2.89}}{2 \cdot - 0.6}$

Rewrite $2.89$ as ${1.7}^{2}$ .

$x = \frac{- 0.7 \pm \sqrt{{1.7}^{2}}}{2 \cdot - 0.6}$

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

$x = \frac{- 0.7 \pm 1.7}{2 \cdot - 0.6}$

Multiply $2$ by $- 0.6$ .

$x = \frac{- 0.7 \pm 1.7}{- 1.2}$

Simplify $\frac{- 0.7 \pm 1.7}{- 1.2}$ .

$x = \frac{0.7 \pm 1.7}{1.2}$

Multiply by $1$ .

$x = \frac{1 (0.7 \pm 1.7)}{1.2}$

Factor $1.2$ out of $1.2$ .

$x = \frac{1 (0.7 \pm 1.7)}{1.2 (1)}$

Separate fractions.

$x = \frac{1}{1.2} \cdot \frac{0.7 \pm 1.7}{1}$

Divide $1$ by $1.2$ .

$x = 0.8\overline{3} (\frac{0.7 \pm 1.7}{1})$

Divide $0.7 \pm 1.7$ by $1$ .

$x = 0.8\overline{3} (0.7 \pm 1.7)$

Step 5

The final answer is the combination of both solutions.

$x = 2, - 0.8\overline{3}$