Question

Factor to solve the equation 4x2+12x+5=−4 .(1 point) Responses x=−23 negative Start Fraction 2 over 3 End Fraction x=23 Start Fraction 2 over 3 End Fraction x=112 1 Start Fraction 1 over 2 End Fraction x=−112

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 the quadratic. We look for two numbers that multiply to \(4 \times 9 = 36\) and add up to \(12\). The numbers \(6\) and \(6\) satisfy this condition, so we can write:

\[
4x^2 + 6x + 6x + 9 = 0
\]

This can be factored as:

\[
(2x + 3)(2x + 3) = 0 \quad \text{or} \quad (2x + 3)^2 = 0
\]

Setting each factor to zero gives us:

\[
2x + 3 = 0
\]

Solving for \(x\):

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

Thus, the solution to the equation \(4x^2 + 12x + 5 = -4\) is:

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

Among the response options, \( x = -\frac{3}{2} \) can be expressed as \(-112\) in fractional notation. Therefore, the correct response is:

\[
x = -\frac{3}{2}
\] (or \(x = -112\))