Solve Using the Quadratic Formula 4x^2+10x=-2

$4 x^{2} + 10 x = - 2$

Step 1

Add $2$ to both sides of the equation.

$4 x^{2} + 10 x + 2 = 0$

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 $a = 4$ , $b = 10$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{- 10 \pm \sqrt{10^{2} - 4 \cdot (4 \cdot 2)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $10$ to the power of $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 4 \cdot 4 \cdot 2}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{- 10 \pm \sqrt{100 - 16 \cdot 2}}{2 \cdot 4}$

Multiply $- 16$ by $2$ .

$x = \frac{- 10 \pm \sqrt{100 - 32}}{2 \cdot 4}$

Subtract $32$ from $100$ .

$x = \frac{- 10 \pm \sqrt{68}}{2 \cdot 4}$

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$x = \frac{- 10 \pm \sqrt{4 (17)}}{2 \cdot 4}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 10 \pm \sqrt{2^{2} \cdot 17}}{2 \cdot 4}$

Pull terms out from under the radical.

$x = \frac{- 10 \pm 2 \sqrt{17}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 10 \pm 2 \sqrt{17}}{8}$

Simplify $\frac{- 10 \pm 2 \sqrt{17}}{8}$ .

$x = \frac{- 5 \pm \sqrt{17}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 5 \pm \sqrt{17}}{4}$

Decimal Form:

$x = - 0.21922359 \dots, - 2.28077640 \dots$