Solve Using the Quadratic Formula -5x-2=-2x^2-2x

$- 5 x - 2 = - 2 x^{2} - 2 x$

Step 1

Move all terms to the left side of the equation and simplify.

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

Add $2 x^{2}$ to both sides of the equation.

$- 5 x - 2 + 2 x^{2} = - 2 x$

Add $2 x$ to both sides of the equation.

$- 5 x - 2 + 2 x^{2} + 2 x = 0$

Add $- 5 x$ and $2 x$ .

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

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 $a = 2$ , $b = - 3$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 2 \cdot - 2$ .

Multiply $- 4$ by $2$ .

$x = \frac{3 \pm \sqrt{9 - 8 \cdot - 2}}{2 \cdot 2}$

Multiply $- 8$ by $- 2$ .

$x = \frac{3 \pm \sqrt{9 + 16}}{2 \cdot 2}$

Add $9$ and $16$ .

$x = \frac{3 \pm \sqrt{25}}{2 \cdot 2}$

Rewrite $25$ as $5^{2}$ .

$x = \frac{3 \pm \sqrt{5^{2}}}{2 \cdot 2}$

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

$x = \frac{3 \pm 5}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{3 \pm 5}{4}$

Step 5

The final answer is the combination of both solutions.

$x = 2, - \frac{1}{2}$