Question

solve $0 = 4x^2 + 12x + 9$
select the equation that shows the correct substitution of $a$, $b$, and $c$ in the quadratic formula
$x = \frac{12 \pm \sqrt{12^2 - 4(4)(9)}}{2(4)}$
$x = \frac{-12 \pm \sqrt{12^2 + 4(4)(9)}}{2(4)}$
$x = \frac{-12 \pm \sqrt{12^2 - 4(4)(9)}}{2(4)}$
simplify the expression to solve the equation.
$x = \boxed{}$
done

Explanation:

Step1: Identify a, b, c

For $ax^2+bx+c=0$, here $a=4$, $b=12$, $c=9$.

Step2: Substitute into quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values: $x=\frac{-12\pm\sqrt{12^2-4(4)(9)}}{2(4)}$

Step3: Calculate discriminant

Compute $12^2-4(4)(9)=144-144=0$

Step4: Solve for x

$x=\frac{-12\pm\sqrt{0}}{8}=\frac{-12}{8}=-\frac{3}{2}$

Answer:

The correct substitution is $\boldsymbol{\frac{-12\pm\sqrt{12^2-4(4)(9)}}{2(4)}}$, and the solution to the equation is $\boldsymbol{-\frac{3}{2}}$