Question

Solve the equation by completing the square m^2+6m-77=-5

Answer 1

Maybe you thought about this:
m^2+6m-77+5=0 => m^2+6m-72=0 => m^2+ 2*3*m+3^2-3^2-72=0
=> m^2+2*3*x+3^2= (m+3)^2 this is the complete square of the binomial, we will still keep it =>
(m+3)^2 -9 -72=0 => (m+3)^2 - 81 = 0 => (m+3)^2 - 9^2 = 0
Now we got the difference squares, it mean a^2 - b^2 = (a-b) (a+b)
In according to this => (m+3-9) (m+3+9) = 0 =>
(m-6) (m+12)=0 => m-6=0 or m+12=0 => m1=6 or m2= -12 !!!!
Are you satisfied with this solution?