Question

solve by completing the square.
4u² + 112u + 44 = 0
write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
u = or u =
submit

Explanation:

Step1: Divide by coefficient of \(u^2\)

Divide the entire equation \(4u^2 + 112u + 44 = 0\) by \(4\) to get \(u^2 + 28u + 11 = 0\). Then, move the constant term to the right: \(u^2 + 28u = -11\).

Step2: Complete the square

Take half of the coefficient of \(u\) (which is \(28\)), square it: \((\frac{28}{2})^2 = 14^2 = 196\). Add this to both sides: \(u^2 + 28u + 196 = -11 + 196\). The left side becomes a perfect square: \((u + 14)^2 = 185\).

Step3: Solve for \(u\)

Take the square root of both sides: \(u + 14 = \pm\sqrt{185}\). Then, solve for \(u\): \(u = -14 \pm\sqrt{185}\). Calculate the decimal values: \(\sqrt{185} \approx 13.60\), so \(u \approx -14 + 13.60 = -0.40\) or \(u \approx -14 - 13.60 = -27.60\).

Answer:

\(u \approx -0.40\) or \(u \approx -27.60\) (or in exact form \(u = -14 + \sqrt{185}\) or \(u = -14 - \sqrt{185}\))