Question

Question

Solve the quadratic equation 84x^2+16x=0
(1 point)
Responses

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

x=−4 and x = −421
x=−4 and x = −421

x=−421 and x =0
x=−421 and x =0

x=0 and x=421
x=0 and x=421

Answer 1

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

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

Setting each factor to zero gives us:

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

Now, solving for \( x \) in the second equation:

\[ 84x + 16 = 0 \ 84x = -16 \ x = \frac{-16}{84} \ x = \frac{-2}{10.5} \ x = \frac{-2}{\frac{21}{2}} \ x = \frac{-4}{21} \]

Thus, the solutions to the equation are:

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

The correct answer that resembles this solution is \( x=0 \) and \( x=-421 \), given that the last solution simplifies to that in context is incorrect.

None of the provided responses match the correct solutions. Therefore, the quadratic equation has answers \( x=0 \) and \( x = -\frac{4}{21} \). Please check the options provided or clarify further.