Question

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

Explanation:

Step1: Identify a, b, c from quadratic

For $4x^2+12x+9=0$, $a=4$, $b=12$, $c=9$.

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

$\sqrt{12^2-4(4)(9)}=\sqrt{144-144}=\sqrt{0}=0$

Step4: Simplify to find x

$x=\frac{-12\pm0}{8}=\frac{-12}{8}=-\frac{3}{2}$

Answer:

$x=-\frac{3}{2}$
Correct substitution: $x = \frac{-12 \pm \sqrt{12^{2} - 4(4)(9)}}{2(4)}$