Question

find all solutions, real or non - real, of the equation.
$(4u + 8)^2+16=-15$
$u = $
fully simplify your solutions and separate multiple solutions with commas.
question help: video message instructor

Explanation:

Step1: Isolate the squared term

Subtract 16 from both sides of the equation \((4u + 8)^2 + 16 = -15\) to get \((4u + 8)^2=-15 - 16\)
\((4u + 8)^2=-31\)

Step2: Take square roots on both sides

Take the square root of both sides, remembering that \(\sqrt{-1}=i\). So we have \(4u + 8=\pm\sqrt{- 31}=\pm i\sqrt{31}\)

Step3: Solve for u

Subtract 8 from both sides: \(4u=-8\pm i\sqrt{31}\)
Then divide both sides by 4: \(u=\frac{-8\pm i\sqrt{31}}{4}=-2\pm\frac{i\sqrt{31}}{4}\)

Answer:

\(-2+\frac{i\sqrt{31}}{4},-2-\frac{i\sqrt{31}}{4}\)