Solve Using the Quadratic Formula x^2+11x+4=0

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

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 $a = 1$ , $b = 11$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (1 \cdot 4)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 1 \cdot 4}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 4}}{2 \cdot 1}$

Multiply $- 4$ by $4$ .

$x = \frac{- 11 \pm \sqrt{121 - 16}}{2 \cdot 1}$

Subtract $16$ from $121$ .

$x = \frac{- 11 \pm \sqrt{105}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 11 \pm \sqrt{105}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 11 \pm \sqrt{105}}{2}$

Decimal Form:

$x = - 0.37652461 \dots, - 10.62347538 \dots$