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x^2-6x+9=5

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here is how you proceed to complete the square on this equation (means to make the expression that involve x a complete square. also means to know how much you need to add to BOTH sides of the equation to make it a complete square if it is NOT ALREADY a complete square)

first look for x (not x2 ) and read its coefficient (means the number that is multipled by x) which is -6

second take half this number -6/2 which is -3

third square the result (-3)2 which is 9

Now you can see that there is already 9 on the right side of the given equation, so there is no need to add 9 to BOTH sides! and that means the right side is already a complete square and so we can write it like follows:

                                                               (x-3)2 = 5

(note that x is the square root of x2 and - sign is the sign of the term that invole x and 3 is the square root of 9 - the number that make the right side a complete square)

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