Question

using the quadratic formula to solve (x^2 - 20 = 2x), what are the values of (x)?

• (1 pm sqrt{21}i)
• (-1 pm sqrt{19}i)
• (1 pm 2sqrt{19}i)
• (1 pm sqrt{19}i)

Explanation:

⚡ Using what you learned: quadratic formula and its applications

Step 1: Standard Form

$$ x^2 - 2x + 20 = 0 $$

$$ a = 1, \quad b = -2, \quad c = 20 $$

Step 2: Apply Quadratic Formula

$$ x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(20)}}{2(1)} $$

$$ x = \frac{2 \pm \sqrt{4 - 80}}{2} $$

$$ x = \frac{2 \pm \sqrt{-76}}{2} $$

Step 3: Simplify Radical

$$ \sqrt{-76} = \sqrt{-1 \cdot 4 \cdot 19} = 2i\sqrt{19} $$

$$ x = \frac{2 \pm 2i\sqrt{19}}{2} $$

$$ x = 1 \pm i\sqrt{19} $$

Answer:

\(1 \pm \sqrt{19}i\) (or \(1 \pm i\sqrt{19}\))