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

2 Answers
sankarankalyanam
Oct 22, 2017

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

Phillip E.
Oct 22, 2017

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)

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