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Chapter 6: Problem 35

Solve each equation using the zero-product principle. \((4 x+5)(x-2)=0\)

Short Answer

Expert verified
The solutions to the equation are \(x = -5/4\) and \(x = 2\).

Step by step solution

01

Setting First Factor Equal to Zero

Set \(4x + 5 = 0\) and solve for x. This can be done by subtracting 5 from both sides of the equation and then dividing by 4 to isolate x.
02

Solving First Factor

After subtracting 5 from both sides, the equation becomes \(4x = -5\). Dividing by 4, we get \(x = -5/4\) or -1.25.
03

Setting Second Factor Equal to Zero

Now set \(x - 2 = 0\) and solve for x. This can be done by adding 2 to both sides of the equation.
04

Solving Second Factor

After adding 2 to both sides, the equation becomes \(x = 2\). So, the second root of the equation is 2.

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