Question

complete the square f(x)x^2+6-16

Answer 1

solution:

$x^2+6x=16\\

x^2+6x-16=0\\

solving for variable'x'\\

add 16 to each side of the equation\\

x^2+6x+16-16=0+16\\

x^2+6x=16\\

the x term is 6x.take half its cofficient(3),square it (9)and it to both side\\

add 9 to each side of the equation\\

6x+9+x^2=16+9\\

x^2+6x+9=25$$factor a ferfect square of the right side 5\\

this problem into teo subproblem by (x+3) equal to 5 and -5\\

sub problem 1\\

x+3=5\\

x=5-3\\

x=2\\

sub problem 2\\

x+3=-5\\

x=-5-3\\

x=-8\\

the solution to the problem is based on the solution from the sub problem is\\

x={2,-8}$