Solve Using the Quadratic Formula f(x)=x^2+7x+9

$f (x) = x^{2} + 7 x + 9$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 7$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot 9)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot 9}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 9}}{2 \cdot 1}$

Multiply $- 4$ by $9$ .

$x = \frac{- 7 \pm \sqrt{49 - 36}}{2 \cdot 1}$

Subtract $36$ from $49$ .

$x = \frac{- 7 \pm \sqrt{13}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm \sqrt{13}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 7 \pm \sqrt{13}}{2}$

Decimal Form:

$x = - 1.69722436 \dots, - 5.30277563 \dots$