Solve Using the Quadratic Formula 4a^2+9a+1=0

$4 a^{2} + 9 a + 1 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 4$ , $b = 9$ , and $c = 1$ into the quadratic formula and solve for $a$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (4 \cdot 1)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

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

$a = \frac{- 9 \pm \sqrt{81 - 4 \cdot 4 \cdot 1}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$a = \frac{- 9 \pm \sqrt{81 - 16 \cdot 1}}{2 \cdot 4}$

Multiply $- 16$ by $1$ .

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

Subtract $16$ from $81$ .

$a = \frac{- 9 \pm \sqrt{65}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$a = \frac{- 9 \pm \sqrt{65}}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$a = \frac{- 9 \pm \sqrt{65}}{8}$

Decimal Form:

$a = - 0.11721778 \dots, - 2.13278221 \dots$