Solve Using the Quadratic Formula 5x^2=-11x-4

$5 x^{2} = - 11 x - 4$

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

Add $11 x$ to both sides of the equation.

$5 x^{2} + 11 x = - 4$

Add $4$ to both sides of the equation.

$5 x^{2} + 11 x + 4 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 5$ , $b = 11$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (5 \cdot 4)}}{2 \cdot 5}$

Simplify.

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 5 \cdot 4}}{2 \cdot 5}$

Multiply $- 4$ by $5$ .

$x = \frac{- 11 \pm \sqrt{121 - 20 \cdot 4}}{2 \cdot 5}$

Multiply $- 20$ by $4$ .

$x = \frac{- 11 \pm \sqrt{121 - 80}}{2 \cdot 5}$

Subtract $80$ from $121$ .

$x = \frac{- 11 \pm \sqrt{41}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{- 11 \pm \sqrt{41}}{10}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 11 \pm \sqrt{41}}{10}$

Decimal Form:

$x = - 0.45968757 \dots, - 1.74031242 \dots$