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

Responses

x=23
Start Fraction 2 over 3 End Fraction

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

x=112
1 Start Fraction 1 over 2 End Fraction

x=−23

1 answer

To solve the equation \(4x^2 + 12x + 5 = -4\), we first move all terms to one 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. Notice that \(4x^2 + 12x + 9\) can be factored as:

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

Setting the factored form equal to zero gives us:

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

Taking the square root of both sides, we have:

\[ 2x + 3 = 0 \]

Solving for \(x\):

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

Now we can express \(-\frac{3}{2}\) as mixed fraction format, which corresponds to the negative one and a half.

Verifying the options provided, it matches:

Negative one Start Fraction 1 over 2 End Fraction

Thus, the correct answer is:

x = -\frac{3}{2}