Question

Factor to solve the equation 4x^2+12x+5=−4 .(1 point)
x=-2/3
x=2/3
x=1 1/2
x=-1 1/2

Answer 1

choose from one of the answers listed

Answer 2

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

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

This simplifies to:

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

Next, we can factor the quadratic equation:

\[
4x^2 + 12x + 9 = (2x + 3)(2x + 3) = (2x + 3)^2 = 0
\]

Now, set the factor equal to zero:

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

Taking the square root of both sides gives:

\[
2x + 3 = 0
\]

Solving for \(x\):

\[
2x = -3 \\
x = -\frac{3}{2} \\
x = -1.5
\]

In fractional form, this is:

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

Among the options given:

- \(x = -2/3\)
- \(x = 2/3\)
- \(x = 1 \frac{1}{2}\)
- \(x = -1 \frac{1}{2}\)

The correct answer is:

\[
x = -1 \frac{1}{2}
\]

Thus, the solution to the equation is \(x = -\frac{3}{2}\) or \(x = -1.5\).

Answer 3

The correct option from the list provided is:

**x = -1 1/2** (which is equivalent to \(x = -\frac{3}{2}\)).