Asked by Smartypants
Solve by factoring.s squared plus 8 s plus 15 equals 0Question content area bottomPart 1The solution is s =enter your response here.(Use a comma to separate answers as needed.)
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Answered by
GPT-4o mini
To solve the quadratic equation \( s^2 + 8s + 15 = 0 \) by factoring, we need to factor the quadratic expression on the left.
1. We look for two numbers that multiply to \( 15 \) (the constant term) and add to \( 8 \) (the coefficient of \( s \)).
2. The numbers \( 3 \) and \( 5 \) fit, since \( 3 \times 5 = 15 \) and \( 3 + 5 = 8 \).
Thus, we can factor the quadratic expression as:
\[
(s + 3)(s + 5) = 0
\]
3. Now, we set each factor equal to zero:
\[
s + 3 = 0 \quad \text{or} \quad s + 5 = 0
\]
4. Solving these gives us:
\[
s = -3 \quad \text{or} \quad s = -5
\]
Therefore, the solution to the equation \( s^2 + 8s + 15 = 0 \) is:
\[
s = -3, -5
\]
So you can enter your response as:
\(-3, -5\)
1. We look for two numbers that multiply to \( 15 \) (the constant term) and add to \( 8 \) (the coefficient of \( s \)).
2. The numbers \( 3 \) and \( 5 \) fit, since \( 3 \times 5 = 15 \) and \( 3 + 5 = 8 \).
Thus, we can factor the quadratic expression as:
\[
(s + 3)(s + 5) = 0
\]
3. Now, we set each factor equal to zero:
\[
s + 3 = 0 \quad \text{or} \quad s + 5 = 0
\]
4. Solving these gives us:
\[
s = -3 \quad \text{or} \quad s = -5
\]
Therefore, the solution to the equation \( s^2 + 8s + 15 = 0 \) is:
\[
s = -3, -5
\]
So you can enter your response as:
\(-3, -5\)
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