Complete the Square: x^2+6x=7

X^2+6x=7 Half the middle term which 6. And square the result 6/2 = 3 3^2 = 9 This 9 will be added in the left side after the 6x. And also to be added at the right side. Because there is a rule that what you did in left side is you need to to in the right side to be equal. X^2+6x + 9 = 7 + 9 Convert the left side equation into squared and the other side add the two numbers (X+3) ^2 = 16 Squared both sides to remove tye 2 X+3 = + and - 4 You need to right two signs

So if in ax^2+bx+c form then

for the completing the square

(b/2) ^2=c so

if b=6 then

b/2=6/2=3

(b/2) ^2 = (6/2) ^2 = (3) ^2=9

so c=9

x^2+6x=7

add 9 to both sides

x^2+6x+9=16

so factor and get

(x+3) ^2=16

for fun solve

16=4^2

(x+3) ^2=4^2 or - 4

square root both sides

x+3=4 or - 4

solve 2 equaitons

1. x+3=4

sutract 3 from both sides

x=-1

2. x+3=-4

subtract 3 from both sides

x=-7

x=-1 or - 7

solution set=S=x=-1,-7

answer is x^2+6x+9=16