Solve the quadratic equation 84x^2+16x=0

Question

(1 point)
Responses

x=−4/21 and x =0
x=−4/21 and x =0

x=−4 and x = −4/21
x=−4 and x = −4/21

x=0 and x=4
x=0 and x=4

x=0 and x=4/21

Answer 1

To solve the quadratic equation \(84x^2 + 16x = 0\), we can factor out the common term, which is \(x\):

\[ x(84x + 16) = 0 \]

Setting each factor equal to zero gives us two possible solutions:

1. \(x = 0\)
2. \(84x + 16 = 0\)

Now, solving the second equation:

\[ 84x + 16 = 0 \implies 84x = -16 \implies x = -\frac{16}{84} \]

Simplifying \(-\frac{16}{84}\):

\[ -\frac{16}{84} = -\frac{4}{21} \]

Thus, the solutions to the equation \(84x^2 + 16x = 0\) are:

\[ x = 0 \quad \text{and} \quad x = -\frac{4}{21} \]

So the correct response is:

x = −4/21 and x = 0.