Question

the solution to (x^2 - 10x = 24) is 12 or -2.

the solution to (2x^2 - 11 = 87) is 7 or -7.

the solution to (3x^2 - 12x + 24 = 0) is

• 7 or -7
• (2 + 2i) or (2 - 2i)
• 12 or -2

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Simplify the equation

Divide the entire equation by \(3\):

$$ x^2 - 4x + 8 = 0 $$

Step 2: Apply the quadratic formula

Using \(a = 1\), \(b = -4\), and \(c = 8\):

$$ x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(8)}}{2(1)} $$

$$ x = \frac{4 \pm \sqrt{16 - 32}}{2} $$

$$ x = \frac{4 \pm \sqrt{-16}}{2} $$

Step 3: Simplify with complex numbers

$$ x = \frac{4 \pm 4i}{2} $$

$$ x = 2 \pm 2i $$

Answer:

\(2 + 2i\) or \(2 - 2i\)