SOLUTION: Solve the quadratic equation by completing the square. 4x^2-28x+49=5

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Question 974267: Solve the quadratic equation by completing the square.
4x^2-28x+49=5
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
THE SOLUTION:
4x%5E2-28x%2B49=5
4x%5E2-28x=5-49
4x%5E2-28x=-44
4x%5E2-28x%2B49=-44%2B49
%282x-7%29%5E2=5
2x-7=%22+%22+%2B-+sqrt%285%29
2x=7+%2B-+sqrt%285%29
x=%287+%2B-+sqrt%285%29%29%2F2

THE EXPLANATION:
If 4x%5E2-28x is to be part of a square %28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2 ,
it may be that a=2x-->a%5E2=4x%5E2 ,
and in that case, it must be that 2ab=-28x
system%282ab=-28x%2Ca=2x%29-->2%282x%29b=-28x-->%284x%29b=-28x-->b=-28x%2F%224+x%22-->b=-7-->b%5E2=49 ,
and we have %282x-7%29%5E2=4x%5E2-28x%2B49 ,
so to complete the square suggested by 4x%5E2-28x=-44 ,
and still have an equivalent equation,
we must add 49 to both sides of the equal sign.