Solve Using the Quadratic Formula 4x^2=-9x-4

$4 x^{2} = - 9 x - 4$

Step 1

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

Add $9 x$ to both sides of the equation.

$4 x^{2} + 9 x = - 4$

Add $4$ to both sides of the equation.

$4 x^{2} + 9 x + 4 = 0$

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 $a = 4$ , $b = 9$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (4 \cdot 4)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 4 \cdot 4}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{- 9 \pm \sqrt{81 - 16 \cdot 4}}{2 \cdot 4}$

Multiply $- 16$ by $4$ .

$x = \frac{- 9 \pm \sqrt{81 - 64}}{2 \cdot 4}$

Subtract $64$ from $81$ .

$x = \frac{- 9 \pm \sqrt{17}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 9 \pm \sqrt{17}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 9 \pm \sqrt{17}}{8}$

Decimal Form:

$x = - 0.60961179 \dots, - 1.64038820 \dots$