To complete the​ square, what number should be added to both sides of the​ equation?

Question

To complete the​ square, what number should be added to both sides of the​ equation?

3x^2+2x-5=0

Answer 1

3x^2 +2x -5 = 0

divide by 3 to get

x^2 + 2x/3 -5/3 = 0

take half of (2/3) and square it: 1/3 is half of 2/3, (1/3)^2= 1/9

add 1/9 to both sides

x^2 + 2x/3 + 1/9 -5/3 = 1/9

(x+1/3)^2 = 1/9+ 5/3 = 1/9+15/9 = 16/9

x+1/3 = + or - sqr(16/9) = + 4/3

x = -1/3 + 4/3

x = 1 or -5/3

or

3x^2 + 2x -5 = 0

add half of 2/3 = 1/3 to both sides

3x^2 +2x -5 +1/3 = 1/3

3x^2 +2x + 1/3 = 1/3 +5 = 1/3+15/3 = 16/3

(xsqr3 + 1//sqr3)^2 = 16/3

xsqr3 +1/sqr3 = + or - sqr(16/3)

xsqr3 = -1/sqr3 + or - 4/sqr3 = -5/sqr3 or 3/sqr3

x = (-5/sqr3)/sqr3 or (3/sqr3)/sqr3

x = -5/3 or 1

IF you really want to stick with the original equation with only integer coefficients then add 1/3 to both sides

but you can't factor the completed square into integer factors

so, if you divide by 3 to get the x^2 term to have 1 as its coefficient, then add 1/9 to both sides