Question

the solution to $x^2 - 10x = 24$ is ✔ 12 or -2. complete the solution to $2x^2 - 11 = 87$ is ✔ 7 or -7. complete the solution to $3x^2 - 12x + 24 = 0$ is. done ✔

Explanation:

Step1: Simplify the quadratic equation

Divide all terms by 3:
$$\frac{3x^2}{3} - \frac{12x}{3} + \frac{24}{3} = \frac{0}{3}$$
$$x^2 - 4x + 8 = 0$$

Step2: Use quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for $ax^2+bx+c=0$. Here $a=1$, $b=-4$, $c=8$.
First calculate discriminant:
$$\Delta = b^2 - 4ac = (-4)^2 - 4(1)(8) = 16 - 32 = -16$$

Step3: Solve for complex roots

$$x = \frac{4 \pm \sqrt{-16}}{2} = \frac{4 \pm 4i}{2}$$
Simplify the fraction:
$$x = 2 \pm 2i$$

Answer:

$2 + 2i$ or $2 - 2i$