Completing the square is based on the fact that when a binomial is squared, there is a specific relationship between the coefficients of the 2nd and 3rd terms."
(x - 5)^2 = x^2 - 10x + 25(x−5)2=x2−10x+25
Note that (-10) divided by 2 and then squared gives 25.
We have 2x^2 + 3x = 20" divide by 2 first to get " x^22x2+3x=20 divide by 2 first to get x2
x^2 + 3/2 x " " = 10" "x2+32x =10 (3/2)÷ 2 = (3/4)(32)÷2=(34)
Add (3/4)^2(34)2 to both sides
x^2 + 3/2 x + color(red)((3/4)^2) = 10 + color(red)((3/4)^2)x2+32x+(34)2=10+(34)2
The left side can now be written as "(binomial)"^2(binomial)2
(x + 3/4)^2 " " = 169/16(x+34)2 =16916
x + 3/4 = +-(13/4)" find the square root of both sides"x+34=±(134) find the square root of both sides
x = 13/4 - 3/4 " or "x = -13/4 - 3/4x=134−34 or x=−134−34
x = 10/4 " or " x = -16/4x=104 or x=−164
x = 2 1/2 " or "x = -4x=212 or x=−4
