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How to perform formula operation on the equation?

1.How to formulate a formula that contains only one parameter?

1/4 m^2 + m + 5

How to get:

1/4 (m + 2)^2 + 4

2.How to formulate a formula that contains two parameter?

59 - 4 x + x^2 + 16 y + y^2

how to get:

(x - 2)^2 + (y + 8)^2 - 9
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1 Answer 1

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For the first one

expr = 1/4* m^2 + m + 5;
ResourceFunction["CompleteSquare"][expr, m]

Mathematica graphics

For the second one, the above ResourceFunction does not work since it only supports one variable. But you can use

expr = 59 - 4 x + x^2 + 16 y + y^2;
CompleteTheSquare[expr, {x, y}]

Mathematica graphics

Where the above function is in the answer by Simon in this post Defining a function that completes the square given a quadratic polynomial expression

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  • $\begingroup$ expr = 59 - 4 x + x^2 + 16 y + y^2; CompleteTheSquare[expr, {x, y}]This code does not calculate the answer $\endgroup$
    – csn899
    Mar 10, 2023 at 1:45
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    $\begingroup$ @csn899 did you first evaluate the code given in the link?? it works for me on V 13.2. As I mentioned, I using code posted in another answer. !Mathematica graphics $\endgroup$
    – Nasser
    Mar 10, 2023 at 1:45
  • $\begingroup$ Do I need to be connected to the network to use this function(ResourceFunction)? $\endgroup$
    – csn899
    Mar 10, 2023 at 5:18
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    $\begingroup$ @csn899 Yes. But I think there is also a way to download the function to your PC and use it so that you do not need to be connected all the time. I do not know how myself but others would. That is one thing I do not like about ResourceFunctions and that is why I do not use them myself in my code. If you search this site you might find something. If not, you could always make new question about this issue. $\endgroup$
    – Nasser
    Mar 10, 2023 at 5:32

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