Express x² - 10x + 32 in the form (x-h)² + g
1. Get the coefficient of x, which is -10
2. Multiply it by , get -10 = -5
3. Square this result, get (-5)² = 25
4. Add this value, 25, then subtract it, after the 10x
(this just amounts to adding nothing, or zero)
x² - 10x + 25 - 25 + 32
Put parentheses around the first three terms
(x² - 10x + 25) - 25 + 32
Combine the two numbers on the right:
(x² - 10x + 25) + 7
Factor the trinomial:
(x - 5)(x - 5) + 7
Since the two factors are the same we write it just once squared:
(x - 5)² + 7
That's it.
Edwin