Question
Factor to solve the equation 4x2+12x+5=−4 .(1 point)Responsesx=23Start Fraction 2 over 3 End Fractionx=1121 Start Fraction 1 over 2 End Fractionx=−112negative 1 Start Fraction 1 over 2 End Fractionx=−23negative Start Fraction 2 over 3 End Fraction
Answers
GPT-4o mini
To solve the equation \( 4x^2 + 12x + 5 = -4 \), we first move all terms to one side of the equation to set it to zero:
\[
4x^2 + 12x + 5 + 4 = 0
\]
This simplifies to:
\[
4x^2 + 12x + 9 = 0
\]
Next, we can factor this quadratic equation. Notice that \( 4x^2 + 12x + 9 \) can be rewritten as:
\[
(2x + 3)(2x + 3) = 0
\]
or
\[
(2x + 3)^2 = 0
\]
Now, to solve for \( x \), we set the factor equal to zero:
\[
2x + 3 = 0
\]
Solving for \( x \):
\[
2x = -3
\]
\[
x = -\frac{3}{2}
\]
Thus, the solution to the equation is:
\[
x = -\frac{3}{2}
\]
This corresponds with the option \( x = -1 \frac{1}{2} \) from your responses.
\[
4x^2 + 12x + 5 + 4 = 0
\]
This simplifies to:
\[
4x^2 + 12x + 9 = 0
\]
Next, we can factor this quadratic equation. Notice that \( 4x^2 + 12x + 9 \) can be rewritten as:
\[
(2x + 3)(2x + 3) = 0
\]
or
\[
(2x + 3)^2 = 0
\]
Now, to solve for \( x \), we set the factor equal to zero:
\[
2x + 3 = 0
\]
Solving for \( x \):
\[
2x = -3
\]
\[
x = -\frac{3}{2}
\]
Thus, the solution to the equation is:
\[
x = -\frac{3}{2}
\]
This corresponds with the option \( x = -1 \frac{1}{2} \) from your responses.