The method using completing the square is based on:
(x-y)^2 = x^2 - 2xy +y^2(x−y)2=x2−2xy+y2
(x-6)^2 = x^2 color(red)(-12)x +color(blue)(36) (x−6)2=x2−12x+36 Note that: (color(red)(-12)/2)^2 = color(blue)(36)(−122)2=36
This relationship always exists in squaring a binomial.
x^2 +30x-7 =0" 7 is not the correct constant"x2+30x−7=0 7 is not the correct constant
Move the 7 to the other side and add in the correct constant on both sides.
x^2 color(red)(+30)x color(blue)(+225)= 7 color(blue)(+225)" "(color(red)(30)/2)^2 = color(blue)225x2+30x+225=7+225 (302)2=225
(x+15)^2 = 232" "x^2 +30x+225" is a square"(x+15)2=232 x2+30x+225 is a square
x + 15 = +-sqrt232 " square root both sides"x+15=±√232 square root both sides
Solve for x twice:
x = +sqrt232 -15 = 0.2315x=+√232−15=0.2315
x = - sqrt232 -15 =-30.2315x=−√232−15=−30.2315
