Question

try it applying the quadratic solve 0 = 4x²+12x+9. select the equation that shows the correct substitution of a, b, and c in the quadratic formula. x = (12 ± √(12² - 4(4)(9))) / (2(4)) x = (-12 ± √(12² + 4(4)(9))) / (2(4)) ✔ x = (-12 ± √(12² - 4(4)(9))) / (2(4)) simplify the expression to solve the equation. x = blank done

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

Step4: Simplify the Discriminant

First, calculate the discriminant \(D=12^{2}-4(4)(9)=144 - 144 = 0\).

Step5: Solve for x

Now, substitute \(D = 0\) into the formula:
\(x=\frac{-12\pm\sqrt{0}}{2(4)}=\frac{-12\pm0}{8}=\frac{-12}{8}=-\frac{3}{2}\)

Answer:

\(-\frac{3}{2}\)