Question

solve for u. $u^{2}+7u + 10 = 0$. if there is more than one solution, separate them with commas. if there is no solution, click on
o solution\.

Explanation:

Step1: Identify the quadratic - formula coefficients

For the quadratic equation \(au^{2}+bu + c = 0\), in the equation \(u^{2}+7u + 10=0\), we have \(a = 1\), \(b = 7\), and \(c = 10\).

Step2: Apply the quadratic formula \(u=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)

First, calculate the discriminant \(\Delta=b^{2}-4ac=(7)^{2}-4\times1\times10=49 - 40=9\).
Then, \(u=\frac{-7\pm\sqrt{9}}{2\times1}=\frac{-7\pm3}{2}\).

Step3: Find the two solutions

For the plus - sign: \(u_1=\frac{-7 + 3}{2}=\frac{-4}{2}=-2\).
For the minus - sign: \(u_2=\frac{-7-3}{2}=\frac{-10}{2}=-5\).

Answer:

\(-2,-5\)