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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 on the left side.
The GCF of \(84x^2\) and \(16x\) is \(4x\). Now, we can factor out \(4x\):
\[
84x^2 + 16x = 4x(21x + 4) = 0
\]
Next, we can set each factor equal to zero:
1. \(4x = 0\)
2. \(21x + 4 = 0\)
Solving the first equation:
\[
4x = 0 \implies x = 0
\]
Solving the second equation:
\[
21x + 4 = 0 \implies 21x = -4 \implies x = -\frac{4}{21}
\]
Thus, the solutions are:
\[
x = 0 \quad \text{and} \quad x = -\frac{4}{21}
\]
From the provided options, the correct response is:
**The solutions are x=0 and x=−4/21.**