Question

solve for s.
\\( s^2 + 3s - 18 = 0 \\)
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
\\( s = \square \\)
save answer

Explanation:

Step1: Factor the quadratic equation

We need to factor \(s^2 + 3s - 18 = 0\). We look for two numbers that multiply to \(-18\) and add up to \(3\). The numbers are \(6\) and \(-3\) because \(6\times(-3)=-18\) and \(6 + (-3)=3\). So we can factor the equation as \((s + 6)(s - 3)=0\).

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

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \((s + 6)(s - 3)=0\), we set each factor equal to zero:

• If \(s+6 = 0\), then \(s=-6\).
• If \(s - 3=0\), then \(s = 3\).

Answer:

\(3,-6\)