How do you solve #x^2-24x=10# by completing the square?

2 Answers
Oct 22, 2017

Answer:

# x = 24.4097, -0.4097#

Explanation:

# x^2 -24x = 10#

#x^2 + (2 (x) (-12) ) = 10 #

#x^2 + ( 2 (x) (-12) ) +144 -144 = 10# (Add and subtract 144)#

# x^2 + ( 2 (x)(-12) + (12)^2 = 154#
# (x-12)^2 = 154#
# (x-12) = +-sqrt 154 color (white)(aaa)#taking square root on both sides
#x = 12 +- sqrt154 #
#x = 24.4097, -0.4097#

Oct 22, 2017

Answer:

#x=12+-sqrt(154)#

Explanation:

Completing the square means making the #x^2# and #x# terms take the form #x^2 +2nx +n^2#. Where in this case #n=-12#.

So, #x^2-24x=10# becomes #x^2 -24x+144=10+144#.
So, #(x-12)^2=154#
#x=12+-sqrt(154)#