Question

solve the quadratic equation by completing the square. (enter your answers as a comma - separated list. if an answer does not exist, enter dne.)
$x^{2}+8x + 11 = 0$
$x=$

Explanation:

Step1: Isolate the x - terms

$x^{2}+8x=- 11$

Step2: Find the value to complete the square

The coefficient of $x$ is $8$. Half of it is $\frac{8}{2}=4$, and its square is $4^{2} = 16$. Add 16 to both sides of the equation:
$x^{2}+8x + 16=-11 + 16$

Step3: Rewrite the left - hand side as a perfect square

$(x + 4)^{2}=5$

Step4: Solve for x

$x+4=\pm\sqrt{5}$
$x=-4\pm\sqrt{5}$

Answer:

$-4+\sqrt{5},-4 - \sqrt{5}$