Question

Consider the equation:

0 = x^2 - 10x + 10
1) Rewrite the equation by completing the square.
Your equation should look like (x + a)2 = b or (x - c)2 = d.

Answer 1

x² - 10x + 10 = 0

Isolate the constant term

x² - 10x = -10

Complete the square
• coefficient of the x term: -10
• divide in half: -5
• square it: (-5)² = 5²
• add 5² to both sides, to complete the square and keep the equation balanced:
x² - 10x + 5² = -10 + 5²
(x-5)² = 15

Answer 2

1) We can rewrite the equation as 15=(x-5)^2

2) The solutions to the equation are x=5±15

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