SOLUTION: Solve by completing the square. x^2 = 5x + 2

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Question 104057: Solve by completing the square.
x^2 = 5x + 2
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Transforming the equation,
x%5E2-5x-2=0
Note that,perfect squares have the format,
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2

Thus, comparing this to the equation,
2ab=-5x--------------------------------(1)
and also,
a=x------------------------------------(2)
Substituting (2) to (1),
2bx=-5x
2b=-5
b=-5/2
Then,
%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2=x%5E2-5x%2B%2825%2F4%29
Thus,

x%5E2-5x-2=0
x%5E2-5x%2B%2825%2F4%29=0%2B2%2B%2825%2F4%29
%28x%5E2%2B%2825%2F4%29%29%5E2=33%2F4
x%2B%285%2F2%29=%2B%28sqrt%2833%29%2F2%29 or x%2B%285%2F2%29=-%28sqrt%2833%29%2F2%29
x=-%285%2F2%29%2B%28sqrt%2833%29%2F2%29 or x=-%285%2F2%29-%28sqrt%2833%29%2F2%29