Question

Solve for u: 3u^2+5=-16u
If there is more than one solution separate them with commas.

Answer 1

\[3 u^2+5 = -16 u\]
Subtract -16 u from both sides:
\[3 u^2+16 u+5 = 0\]
Divide both sides by 3:
\[u^2+\frac{16 u}{3}+\frac{5}{3} = 0\]
Subtract 5/3 from both sides:
\[u^2+\frac{16 u}{3} = -\frac{5}{3}\]
Add 64/9 to both sides:
\[u^2+\frac{16 u}{3}+\frac{64}{9} = \frac{49}{9}\]
Factor the left hand side:
\[(u+\frac{8}{3})^2 = \frac{49}{9}\]
Take the square root of both sides:
\[|u+\frac{8}{3}| = \frac{7}{3}\]
Eliminate the absolute value:
u+8/3 = -7/3 or u+8/3 = 7/3
Subtract 8/3 from both sides:
u = -5 or u+8/3 = 7/3
Subtract 8/3 from both sides:
\[\huge u = -5, \frac{1}{3}\]