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

1 answer

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

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

This simplifies to:

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

Now, we can factor this quadratic equation. We notice that \( 4x^2 + 12x + 9 \) can be factored as:

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

Setting this equal to zero gives us:

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

Taking the square root of both sides:

\[ 2x + 3 = 0 \]

Now, solve for \( x \):

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

Now let’s compare this with the potential answers provided:

  1. \( x = \frac{23}{3} \)
  2. \( x = 1\frac{1}{2} \) (which is \( \frac{3}{2} \))
  3. \( x = -1\frac{1}{2} \) (which is \( -\frac{3}{2} \))
  4. \( x = -\frac{2}{3} \)

The correct answer is:

\[ x = -1\frac{1}{2} \quad \text{(which is } -\frac{3}{2} \text{)} \]