Question

solve for u.
$4u^2 + 20u = -25$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
$u = \square$

Explanation:

Step1: Rearrange the equation

First, we move all terms to one side of the equation to set it to zero. The original equation is \(4u^{2}+20u = - 25\). Adding 25 to both sides gives us \(4u^{2}+20u + 25=0\).

Step2: Identify coefficients for quadratic formula

For a quadratic equation of the form \(ax^{2}+bx + c = 0\) (here \(x = u\)), we have \(a = 4\), \(b = 20\), and \(c = 25\). The quadratic formula is \(u=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).

Step3: Calculate the discriminant

The discriminant \(D=b^{2}-4ac\). Substituting the values of \(a\), \(b\), and \(c\) we get:
\(D=(20)^{2}-4\times4\times25\)
\(D = 400-400\)
\(D=0\)

Step4: Solve for \(u\) using quadratic formula

Since the discriminant is zero, there is exactly one real solution. Substituting into the quadratic formula:
\(u=\frac{-20\pm\sqrt{0}}{2\times4}=\frac{-20\pm0}{8}=\frac{-20}{8}=-\frac{5}{2}\)

Answer:

\(-\frac{5}{2}\)