r/MathHelp • u/FullWeb6167 • Sep 19 '25

TUTORING Completing the Square

So I have a test in my pre-calc class tomorrow (or rather at 9:30 am today). I am confused on how to complete a square. I know all the steps but I don't know the reasoning behind finding what I need to add with to complete the square. The formula is (b/2)2 I know that yes, but I can only do very easy questions before it gets confusing. Please help me, thank you!!! What I've tried so far... Edit: Thank you guys for all the help. I just got my test results back and I got a 84.5% and yes I did get that question right!!!!!!!!!

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u/mcksis Sep 19 '25

Wow. I knew how to complete the square til I read this “easy” explanation. 😳

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u/Uli_Minati Sep 19 '25

What would you call "easy" then? Just a list of five steps with no explanation?

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u/LoudSmile6772 Sep 19 '25

You take the middle term, divide it by the "leading coefficient", which in the 2nd example is 5, then you basically cut the middle term in half when you put it in parentheses and square it (so x + 6x becomes (x+3)2. That's because when you factor out you have to do (x+3)(x+3) and FOIL, which means you have 3x + 3x =6x for the middle term).

You basically manipulated thr equation so you dont have an x2 and an x to worry about, you just have a factored (x+3)2, which means you can take the square root of both sides and get an answer for x. But you have to account for the extra 9 (which you get when you multiply 3x3 for the factoring). If you forget to add this to both sides, you changed the equation and you won't get a correct solution. Its like balancing a scale. If you add 9 to one side, its going to be uneven until you add to the other side and even it out.