Question about completing the square (ax^2+bx+c to a(x-h)^2 + k)

Question

anonymous · Answer

The lesson gives me this as an example:
 f(x) = 5x2 +10x + 6

= 5(x2 + 2x) + 6

= 5(x2 +2x + 1 -1) +6

= 5(x2 +2x +1) + 5(-1) + 6

= 5(x +1)2 + 1 

However I dont understand these two steps


= 5(x2 +2x + 1 -1) +6

= 5(x2 +2x +1) + 5(-1) + 6

anonymous · Answer

Why did they add 1 -1?

anonymous · Answer

and to clarify f(x) is on the other side of the equal sign

sidsiddhartha · Answer

they add 1 because they just wnad to make it a square 
$$x^2+2x=(x^2+2.x.1+1^2)-1=(x+1)^2-1\remember\(a+b)^2=a^2+2ab+b^2$$
and when u are adding 1 then u also have to substract one to maintain the equation intact

anonymous · Answer

Oh! Ok, do you know why they did 5(-1) as well?

sidsiddhartha · Answer

because 5 is outside of the bracket add they are multiplying this 5 with things inside the bracket ,so when u are multiplying (-1) with 5 then it will be 5*(-1)

anonymous · Answer

I dont get it still, it looks like they're randomly subtracting 5 from the equation

sidsiddhartha · Answer

$$5[(x+1)^2-1]=5*(x+1)^2+5*(-1)\like ~this\a(b+c)=a*b+a*c$$

sidsiddhartha · Answer

ok now?

anonymous · Answer

yes thanks so much

sidsiddhartha · Answer

yw!!