Question

solve for u.

u² + 9u + 14 = 0

if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

u =

(there is a box for input and a panel with options like fraction, no solution, etc.)

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(14\) and add up to \(9\). The numbers are \(2\) and \(7\) since \(2\times7 = 14\) and \(2 + 7=9\). So we can factor the quadratic equation \(u^{2}+9u + 14 = 0\) as \((u + 2)(u+7)=0\).

Step2: Solve for \(u\) using zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both).
For \((u + 2)(u + 7)=0\), we set each factor equal to zero:

• If \(u+2=0\), then subtracting \(2\) from both sides gives \(u=-2\).
• If \(u + 7=0\), then subtracting \(7\) from both sides gives \(u=-7\).

Answer:

\(u=-2,-7\)