Question

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

x=23
Start Fraction 2 over 3 End Fraction

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

x=112
1 Start Fraction 1 over 2 End Fraction

x=−23

Answer 1

To solve the equation \(4x^2 + 12x + 5 = -4\), we first move all terms to one side of the equation:

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

This simplifies to:

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

Next, we can factor this quadratic equation. Notice that \(4x^2 + 12x + 9\) can be factored as:

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

Setting the factored form equal to zero gives us:

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

Taking the square root of both sides, we have:

\[
2x + 3 = 0
\]

Solving for \(x\):

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

Now we can express \(-\frac{3}{2}\) as mixed fraction format, which corresponds to the negative one and a half.

Verifying the options provided, it matches:

**Negative one Start Fraction 1 over 2 End Fraction**

Thus, the correct answer is:

**x = -\frac{3}{2}**