Question

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

Answer 1

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

\[
4x^2 + 12x + 5 + 4 = 0
\]
\[
4x^2 + 12x + 9 = 0
\]

Next, we can factor the quadratic expression. The expression \( 4x^2 + 12x + 9 \) can be factored by noticing that it is a perfect square trinomial:

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

Now, we can set the factored expression to zero:

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

Taking the square root of both sides gives:

\[
2x + 3 = 0
\]

Now, solving for \( x \):

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

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

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