Question

now, write \\(x^2 - 16x + 64 = -8\\) as \\((x - 8)^2 = -8\\)

take the square root of both sides to get the solutions

\\(\quad \pm \quad \sqrt{2}i\\)

Explanation:

⚡ Using what you learned: completing the square

Step 1: Take the square root of both sides

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

$$ x - 8 = \pm\sqrt{-8} $$

Step 2: Simplify the radical with complex numbers

$$ \sqrt{-8} = i\sqrt{8} = i\sqrt{4 \cdot 2} = 2i\sqrt{2} $$

$$ x - 8 = \pm 2\sqrt{2}i $$

Step 3: Solve for x

$$ x = 8 \pm 2\sqrt{2}i $$

Answer:

First box: 8
Second box: 2