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Chapter 1: Problem 10

Solve each equation in Exercises \(1-14\) by factoring. $$5 x^{2}-20 x=0$$

Short Answer

Expert verified
The solutions to the equation \(5x^{2} - 20x = 0\) are \(x = 0\) and \(x = 4\).

Step by step solution

01

- Rewrite the equation

First, rewrite the quadratic equation by setting it equal to zero. This can be done by subtracting \(20x\) from each side of the equation to get the result: \[5x^{2} - 20x = 0\]. This equation is already in this form.
02

- Factor out the Greatest Common Factor (GCF)

The next step is to factor out the greatest common factor (GCF) from the equation. In this case, the GCF of \(5x^{2}\) and \(20x\) is \(5x\). Factoring out \(5x\) results in: \[5x(x - 4) = 0\]
03

- Solve for x

The final step is to set each factor equal to zero and solve for x. Setting each factor equal to zero yields two possible solutions for x. \[5x = 0 \rightarrow x = 0,\quad x - 4 = 0 \rightarrow x = 4\]

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