Question

factor to solve the equation 4x^2+12x+5=-4
a. -2/3
b. -1 1/2
c. 1 1/2
d. 2/3

Answer 1

To solve the equation \( 4x^2 + 12x + 5 = -4 \), let's first move \(-4\) to the other 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. We notice that the expression \(4x^2 + 12x + 9\) can be rewritten as a perfect square.

The equation can be factored as follows:

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

or

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

Now, set the expression equal to zero:

\[
2x + 3 = 0
\]

Solving for \(x\):

\[
2x = -3
\]

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

This value can also be expressed as \( -1.5 \) or \( -1 \frac{1}{2} \).

Now, looking at the answer choices provided:

a. -2/3
b. -1 1/2
c. 1 1/2
d. 2/3

The correct answer is:

**b. -1 1/2**