How do you solve # x^2-10x+25=0# algebraically?

1 Answer
reudhreghs
Apr 1, 2016

#x = 5#

Explanation:

Start off by writing the brackets #(x + )(x +)#, because you know this will feature in the answer, given that there's an #x^2#.

Now you want to find two numbers that add together to make #-10# and multiply together to make #25#. Use trial and error by writing down or thinking about the factors of #25#, and then which ones add to #-10#. You should come to #-5# and #-5#.

This gives the brackets #(x-5)(x-5)# or #(x-5)^2 = 0#

Now change around the equation to make #x# the subject.

#(x-5)^2 = 0#
#x-5 = sqrt0#
#x-5 = 0#
#x = 5#

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