Solve for x x^2+11x+11=4x

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

Move all terms containing $x$ to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

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

Subtract $4 x$ from $11 x$ .

$x^{2} + 7 x + 11 = 0$

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 $c = 11$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot 11)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

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

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot 11}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 11}}{2 \cdot 1}$

Multiply $- 4$ by $11$ .

$x = \frac{- 7 \pm \sqrt{49 - 44}}{2 \cdot 1}$

Subtract $44$ from $49$ .

$x = \frac{- 7 \pm \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm \sqrt{5}}{2}$

The final answer is the combination of both solutions.

$x = - \frac{7 - \sqrt{5}}{2}, - \frac{7 + \sqrt{5}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7 - \sqrt{5}}{2}, - \frac{7 + \sqrt{5}}{2}$

Decimal Form:

$x = - 2.38196601 \dots, - 4.61803398 \dots$