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

Sagot :

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
apologiabiology
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

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