Question

Factor to solve the equation 4x2+12x+5=−4
.(1 point)
Responses

x=−112
negative 1 Start Fraction 1 over 2 End Fraction

x=−23
negative Start Fraction 2 over 3 End Fraction

x=23
Start Fraction 2 over 3 End Fraction

x=112

Answer 1

To solve the equation \( 4x^2 + 12x + 5 = -4 \), we first rearrange it into standard form by adding 4 to both sides:

\[
4x^2 + 12x + 5 + 4 = 0
\]

This simplifies to:

\[
4x^2 + 12x + 9 = 0
\]

Next, we can factor this quadratic. We look for two numbers that multiply to \( 4 \times 9 = 36 \) and add to \( 12 \). These numbers are \( 6 \) and \( 6 \).

Thus, we can factor the equation as:

\[
(2x + 3)(2x + 3) = 0
\]

or simply:

\[
(2x + 3)^2 = 0
\]

Setting each factor equal to zero gives:

\[
2x + 3 = 0
\]

Solving for \( x \):

\[
2x = -3 \\
x = -\frac{3}{2}
\]

Since neither of the options provided directly corresponds to \(-\frac{3}{2}\), let’s see if it can be expressed in a different form.

The answer \(-\frac{3}{2}\) can be rewritten as \(-1.5\) or as a decimal approximation if comparisons are needed.

However, if we need to check your responses directly, it looks like none of them match. Please confirm if the equation or the choices provided might contain any discrepancies. Based on the factorization, the answer for this quadratic is:

\[
x = -\frac{3}{2}
\]