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

1 Answer
Jun 30, 2015

Answer:

#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#