Question

algebra 2a semester online practice
complete this assessment to review what youve learned. it will not count toward your grade.
which is the solution to the equation $2(x + 4)^2 + 11 = -5$, re - expressed as a complex number in the standard form $a \pm bi$? (1 point)
\bigcirc $-2 \pm 2i\sqrt{2}$
\bigcirc $4 \pm 2i\sqrt{2}$
\bigcirc $-4 \pm 2i\sqrt{2}$
\bigcirc $-4 \pm 4i$

Explanation:

Step1: Isolate the squared term

Subtract 11 from both sides: $2(x + 4)^2 = -5 - 11 = -16$
Divide both sides by 2: $(x + 4)^2 = \frac{-16}{2} = -8$

Step2: Take square roots

Take square root of both sides: $x + 4 = \pm\sqrt{-8}$
Simplify $\sqrt{-8}$: $\sqrt{-8} = \sqrt{8}\cdot\sqrt{-1} = 2\sqrt{2}i$

Step3: Solve for x

Subtract 4 from both sides: $x = -4 \pm 2\sqrt{2}i$

Answer:

-4 ± 2i√2 (corresponding to the option: -4 ± 2i√2)