Question

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

options:
\\((x - 8)^2 = -16\\)
\\((x - 8)^2 = -8\\)
\\((x - 16)^2 = -16\\)
\\((x - 16)^2 = -8\\)

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Identify the perfect square trinomial

The left side of the equation is:

$$ x^2 - 16x + 64 $$

This fits the perfect square trinomial pattern \( a^2 - 2ab + b^2 = (a - b)^2 \), where:

• \( a = x \)
• \( b = 8 \) (since \( 8^2 = 64 \) and \( 2 \cdot x \cdot 8 = 16x \))

Step 2: Rewrite the equation

Factor the left side:

$$ (x - 8)^2 = -8 $$

Answer:

$$ (x - 8)^2 = -8 $$