Solve Using the Quadratic Formula x^2+9x+3=0

$x^{2} + 9 x + 3 = 0$

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 $a = 1$ , $b = 9$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (1 \cdot 3)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 1 \cdot 3}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 3$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot 3}}{2 \cdot 1}$

Multiply $- 4$ by $3$ .

$x = \frac{- 9 \pm \sqrt{81 - 12}}{2 \cdot 1}$

Subtract $12$ from $81$ .

$x = \frac{- 9 \pm \sqrt{69}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 9 \pm \sqrt{69}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 9 \pm \sqrt{69}}{2}$

Decimal Form:

$x = - 0.34668806 \dots, - 8.65331193 \dots$