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Chapter 7: Problem 9

Solve each equation.. \(11 s(s+15)=0\)

Short Answer

Expert verified
The values of 's' that satisfy the equation \(11s(s+15) = 0\) are \(s = 0\) and \(s = -15\).

Step by step solution

01

Understand the zero-product property

Referring to the given equation, 11s(s+15)=0, it can be observed that it is already in a factored form. The zero-product property states that if two numbers multiply to give a product equals zero, at least one of those two numbers must be zero.
02

Apply the zero-product property to find the first solution

We have two factors: 11s and (s+15), and their product equals zero. So, either 11s equals zero, or (s+15) equals zero. Let's first solve for when 11s=0: \(11s = 0\) To find 's', divide both sides of the equation by 11: \(s = \frac{0}{11}\) Thus, the first value of s is: \(s = 0\)
03

Apply the zero-product property to find the second solution

Now, let's solve the equation for the second factor: (s+15)=0. To isolate 's', subtract 15 from both sides of the equation: \(s + 15 - 15 = 0 - 15\) This simplifies to: \(s = -15\) So, the second value of s is -15.
04

State the solution

Therefore, the two values of 's' that satisfy the equation 11s(s+15) = 0 are: \(s = 0\) and \(s = -15\).

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