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Chapter 6: Problem 34

Solve each equation using the zero-product principle. \((x+11)(x-5)=0\)

Short Answer

Expert verified
The solutions of the equation \((x + 11)(x - 5) = 0\) are \(x = -11\) and \(x = 5\).

Step by step solution

01

Set Each Factor Equal to Zero

To use the zero-product property to solve the equation, each factor must be set equal to zero separately, resulting in two equations to solve: \(x + 11 = 0\) and \(x - 5 = 0\).
02

Solve Each Equation

Solve the two equations individually. Start with the first equation \(x + 11 = 0\). To isolate \(x\), subtract 11 from both sides, resulting in \(x = -11\). Next, solve the second equation \(x - 5 = 0\). Add 5 to both sides, resulting in \(x = 5\).
03

Combine the Solutions

The two values obtained, \(x = -11\) and \(x = 5\), are solutions of the original equation.

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