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}
1 answer