Question

Factor to solve the equation 4x2+12x+5=−4
4
𝑥
2
+
12
𝑥
+
5
=
−
4
.(1 point)
Responses

x=23
𝑥
=
2
3
x equals Start Fraction 2 over 3 End Fraction

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

x=−23
𝑥
=
−
2
3
x equals negative Start Fraction 2 over 3 End Fraction

x=112
𝑥
=
1
1
2
x equals 1 Start Fraction 1 over 2 End Fraction

Answer 1

To solve the equation \( 4x^2 + 12x + 5 = -4 \), we first need to rearrange it to set it equal to zero.

1. Move \(-4\) to the left side:
\[
4x^2 + 12x + 5 + 4 = 0
\]
This simplifies to:
\[
4x^2 + 12x + 9 = 0
\]

2. Now factor the quadratic equation:
We can factor \(4x^2 + 12x + 9\) as:
\[
(2x + 3)(2x + 3) = (2x + 3)^2 = 0
\]

3. Set the factor equal to zero:
\[
2x + 3 = 0
\]

4. Solving for \(x\):
\[
2x = -3 \\
x = -\frac{3}{2}
\]

Now we can check which response matches:

Since \( -\frac{3}{2} \) is not listed, we need to check if there was an error. It looks like I simplified incorrectly. Let's also check:

1. Check discriminant or other roots.
From the discriminant:
\[
D = b^2 - 4ac = 12^2 - 4(4)(9) = 144 - 144 = 0
\]
Indicates a double root.

Thus actual computation might be misdone. However checking responses:

Possible options from your responses:
- \(x = -\frac{2}{3}\)
- \(x = -\frac{1}{2}\)

Since my calculations point to exactly:
Final as \(x = -\frac{3}{2}\) is accurate solving. Your input may have slightly miswritten choices leading no right answer alignment here.

Can help re-confirm choices if misconstrued or set if there's precise problems not clear!