Question

solve for s.
$8s^{2}-3s - 5 = 0$
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
$s = $

Explanation:

Step1: Factor the quadratic equation

We try to factor \(8s^2 - 3s - 5 = 0\). We need two numbers that multiply to \(8\times(-5)=-40\) and add up to \(-3\). The numbers are \(-8\) and \(5\).
Rewrite the middle term: \(8s^2 - 8s + 5s - 5 = 0\)
Group the terms: \((8s^2 - 8s)+(5s - 5)=0\)
Factor out common factors: \(8s(s - 1)+5(s - 1)=0\)
Factor out \((s - 1)\): \((8s + 5)(s - 1)=0\)

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

If \((8s + 5)(s - 1)=0\), then either \(8s+5 = 0\) or \(s - 1=0\)

• For \(s - 1=0\), we get \(s = 1\)
• For \(8s+5 = 0\), subtract \(5\) from both sides: \(8s=-5\), then divide both sides by \(8\): \(s=-\frac{5}{8}\)

Answer:

\(1,-\frac{5}{8}\)