complete the square

[soprano]

I don't understand how to do this problem at all.
12x^(2) + 13 x = 4
Can someone help please

I received a reply but I still do not understand where the 361/576 comes from in completing the square.

 

[BigGlenntheHeavy]

$\displaystyle 12x^{2}+13x \ = \ 4 \ \implies \ 12x^{2}+13x-4 \ = \ 0.$

$\displaystyle 12\bigg[x^{2}+\frac{13x}{12}-\frac{1}{3}\bigg] \ = \ 0$

$\displaystyle 12\bigg[\bigg(x+\frac{13}{24}\bigg)^{2}-\frac{361}{576}\bigg] \ = \ 0, \ this \ completes \ the \ square.$

$\displaystyle Check: \ 12\bigg[x^{2}+\frac{26x}{24}+\frac{169}{576}-\frac{361}{576}\bigg] \ = \ 0$

$\displaystyle = \ 12\bigg[x^{2}+\frac{13x}{12}-\frac{192}{576}\bigg] \ = \ 0$

$\displaystyle =12\bigg[x^{2}+\frac{13x}{12}-\frac{1}{3}\bigg] \ = \ 0$

$\displaystyle = \ 12x^{2}+13x-4 \ = \ 0$

$\displaystyle Your \ query: \ \frac{169}{576}+k \ = \ -\frac{1}{3}, \ k \ being \ the \ unknown \ we \ wish \ to \ know.$

$\displaystyle Hence, \ k \ = \ -\frac{1}{3}-\frac{169}{576} \ = \ -\frac{361}{576}, \ capishe.$