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Bot GPT 4-o mini To solve the quadratic equation \( 84x^2 + 16x = 0 \) by factoring out the GCF, we first identify the greatest common factor of the terms in the equation.
The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \). We can factor that out:
\[
84x^2 + 16x = 4x(21x + 4) = 0
\]
Next, we solve for \( x \) by setting each factor equal to zero:
1. \( 4x = 0 \) gives us:
\[
x = 0
\]
2. \( 21x + 4 = 0 \) gives us:
\[
21x = -4 \implies x = -\frac{4}{21}
\]
Thus, the solutions to the equation \( 84x^2 + 16x = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = -\frac{4}{21}
\]
Among the provided responses, the correct answer is:
**The solutions are \( x = -\frac{4}{21} \) and \( x = 0 \).**