Question

solve the equation for all values of x by completing the square. express your answer in simplest form.

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

Explanation:

Step1: Rearrange the equation

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

Step2: Move the constant term

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

Step3: Add square of half - coefficient of x

The coefficient of $x$ is $4$, half of it is $2$, and its square is $4$. Add $4$ to both sides: $x^{2}+4x + 4=11 + 4$.

Step4: Factor the left - hand side

$(x + 2)^{2}=15$

Step5: Solve for x

$x+2=\pm\sqrt{15}$
$x=-2\pm\sqrt{15}$

Answer:

$x=-2+\sqrt{15},x=-2 - \sqrt{15}$