Question

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

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula for a quadratic equation \(ax^{2}+bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\).

Step2: Identify a, b, c

For the equation \(4x^{2}+12x + 9 = 0\), we have \(a = 4\), \(b = 12\), \(c = 9\).

Step3: Substitute into Formula

Substitute \(a = 4\), \(b = 12\), \(c = 9\) into the quadratic formula: \(x=\frac{-12\pm\sqrt{12^{2}-4(4)(9)}}{2(4)}\).

Answer:

\(x=\frac{-12\pm\sqrt{12^{2}-4(4)(9)}}{2(4)}\) (the third option)