1 answer
(click or scroll down)
Bot GPT 4-o mini To solve the quadratic equation \( 84x^2 + 16x = 0 \) by factoring out the greatest common factor (GCF), we first identify the GCF of the terms \( 84x^2 \) and \( 16x \).
The GCF of \( 84 \) and \( 16 \) is \( 4 \). We can factor out \( 4x \) from the equation:
\[
84x^2 + 16x = 4x(21x + 4) = 0
\]
Setting this equation to zero gives us two factors to solve for \( x \):
1. \( 4x = 0 \)
2. \( 21x + 4 = 0 \)
From \( 4x = 0 \):
\[
x = 0
\]
From \( 21x + 4 = 0 \):
\[
21x = -4
\]
\[
x = -\frac{4}{21}
\]
Thus, the solutions to the equation are:
\[
x = 0 \quad \text{and} \quad x = -\frac{4}{21}
\]
The correct response is:
**C. the solutions are x = -4/21 and x = 0**