How do you solve 5x^2 – 100x + 455 = 0 by completing the square?

1 Answer
Alan P.
Jun 30, 2015

x=7
or
x=13

Explanation:

5x^2-100x+455=0

First simplify by dividing both sides by 5
color(white)("XXXX")x^2-20x+91=0

If (x^2-20x) are the first two terms of a spared binomial the third term must be (+100)
color(white)("XXXX")color(white)("XXXX")since (x-a)^2 = x^2-2ax+a^2

Completing the square
color(white)("XXXX")x^2-20x+100 -9 = 0

color(white)("XXXX")(x-10)^2 = 9

Taking the square root of both sides
color(white)("XXXX")x-10 = +-sqrt(9) = +-3

color(white)("XXXX")x=7 or x=13#

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