can someone help with completing the square of x^2 + 6x = 16

Answer 1

"Complete the square" has F-O-I-L fFirst-Outside-Inside-Left) as its foundation.

(a+b)(c+d) = ac + ad + bc + bd

Now, let's include x:

(ax+b)(cx+d) = acx² + adx + bcx + bd

Now, to square a term means to multiply it by itself, so we must have a=c and b=d.

(ax+b)(ax+b) = a²x² +2abx + b²

That tells us how to "complete the square."

Given x^2 + 6x , we have a=1 and 2b=6. That means that b=3.

We now add b² to BOTH sides of the equation:

x² + 6x + 9 = 16 + 9

(x+3)(x+3) = 25

AND ,,, when you solve for x, it can be either x=2 or x=-8.

Answer 2

x² + 6x = 16

x² + 6x + (6/2)² = 16 + (6/2)²