Answer :
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|x=-1,-7}
answer is x^2+6x+9=16
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|x=-1,-7}
answer is x^2+6x+9=16
