Question

solve for u.
4u² + 4 = -17u
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
u =
there are some icons and buttons on the right side of the input box, including fraction, square root, etc., and buttons with 5 and % symbols, and a
o solution\ option.

Explanation:

Step1: Rearrange the equation

First, we need to rewrite the given equation \(4u^{2}+4 = - 17u\) in standard quadratic form \(ax^{2}+bx + c=0\). We add \(17u\) to both sides of the equation:
\(4u^{2}+17u + 4=0\)

Step2: Use the quadratic formula

For a quadratic equation \(ax^{2}+bx + c = 0\), the quadratic formula is \(u=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). In our equation \(4u^{2}+17u + 4 = 0\), we have \(a = 4\), \(b=17\) and \(c = 4\).

First, calculate the discriminant \(\Delta=b^{2}-4ac\):
\(\Delta=(17)^{2}-4\times4\times4\)
\(=289 - 64\)
\(=225\)

Then, find the roots:
\(u=\frac{-17\pm\sqrt{225}}{2\times4}=\frac{-17\pm15}{8}\)

We have two cases:
Case 1: When we take the plus sign:
\(u=\frac{-17 + 15}{8}=\frac{-2}{8}=-\frac{1}{4}\)

Case 2: When we take the minus sign:
\(u=\frac{-17-15}{8}=\frac{-32}{8}=- 4\)

Answer:

\(-4,-\frac{1}{4}\)