Questions: Solve for u. 4 u^2 + 3 = -8 u

Transcript text: Solve for $u$. \[ 4 u^{2}+3=-8 u \]

Solution

Solve for $ u $ in the equation $ 4u^{2} + 3 = -8u $.

Rearranging the equation.

We start with the equation $ 4u^{2} + 3 = -8u $. Moving all terms to one side gives us $ 4u^{2} + 8u + 3 = 0 $.

Factoring the polynomial.

The polynomial $ 4u^{2} + 8u + 3 $ can be factorized as $ (2u + 1)(2u + 3) $.

Finding the solutions.

Setting each factor to zero, we solve $ 2u + 1 = 0 $ and $ 2u + 3 = 0 $, yielding the solutions $ u = -\frac{1}{2} $ and $ u = -\frac{3}{2} $.

The solutions for $ u $ are $ u = -\frac{3}{2}, -\frac{1}{2} $.

The solutions for $ u $ are $ \boxed{-\frac{3}{2}, -\frac{1}{2}} $.

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