Solve 5x2−40x=0

Question

5
𝑥
2
−
40
𝑥
=
0
by factoring out the greatest common factor. Enter your solutions as an integer.(2 points)
x =
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=


x=
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Answer 1

To solve the equation \( 5x^2 - 40x = 0 \) by factoring out the greatest common factor, we first identify the GCF of the two terms.

The terms are \( 5x^2 \) and \( -40x \). The GCF is \( 5x \).

We can factor out \( 5x \) from the equation:

\[ 5x(x - 8) = 0 \]

Now, using the zero product property, we can set each factor equal to zero:

1. \( 5x = 0 \)
2. \( x - 8 = 0 \)

Solving these equations gives:

1. \( x = 0 \)
2. \( x = 8 \)

Thus, the solutions are:

\[ x = 0 \quad \text{and} \quad x = 8 \]

So the final answer is:

• \( x = 0 \)
• \( x = 8 \)