How do you solve #x^2 – 10x = 15# using completing the square?

2 Answers
Jun 22, 2015

Answer:

#x=5+-2sqrt(10)#

Explanation:

#x^2-10x = 15#
#color(white)("XXXX")#If #x^2-10x# are the first two terms of a squared binominal
#color(white)("XXXX")#then the third term must be 25, since
#color(white)("XXXX")##color(white)("XXXX")##(x-a)^2 = x^2-2ax+a^2#
#color(white)("XXXX")#and, in this case #a=5#
#x^2-10xcolor(blue)(+25) = 15+color(blue)(25)#

#(x-5)^2 = 40#

#color(white)("XXXX")#Taking the square root of both sides gives
#x-5 = +-2sqrt(10)#

#color(white)("XXXX")#and finally
#x = 5+-2sqrt(10)#

Jun 22, 2015

Answer:

I found:

#x_1=5+sqrt(40)#
#x_2=5-sqrt(40)#

Explanation:

You can add and subtract #25# to get:
#x^2-10xcolor(red)(+25)color(red)(-25)=15#
#x^2-10x+25=15+25#
#(x-5)^2=40#
#x-5=+-sqrt(40)#
So:
#x_1=5+sqrt(40)#
#x_2=5-sqrt(40)#