x^2 -10x =11
Now we will add and subtract [(X's coefficient)/2]^2
We know that X's coefficient is 10
==> Then, we will add (10/2)^2 = 5^2 = 25 to both sides.
==> x^2 -10x +25 = 11 + 25
==> x^2 -10x +25 = 36
Now we will rewrite the expression as a complete square.
==> (x-5)^2 = 36
Now to solve, we will take the square root of both sides.
==> l x -5 l = l6l
==> x-5 = 6 ==> x = 11
==> -(x-5) = 6 ==> -x+5 = 6 ==> -x = 1 ==> x = -1
Then we have two solutions:
x = { -1, 11}
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