m^2 = -6m - 7 completing the square?

Question

ok so it seems to me like it's going to look something like
(m + 1)(m - 7) = m^2 -7m +1m -7 = m^2 -6m -7. But the answer reads m= -3 plus/minus radical 2...?

I can use some help on understanding whats going on here.

Answer 1

m^2 -6m -7 notice wher the equal sign is???
is not correct, when you move the 6m and 7 over it would be
m^2 +6m +7 = 0 , which does not factor over the reals

Complete the square
m^2 +6m +__ = -7+ ____ ===> (6/2)^2 = 9
m^2 +6m +_9_ = -7+ _9_
(m+3)^2 = 2
m+3 = +/- v2
m = -3 +/- v2

=]

Answer 2

m²+6m+7=0
We need two numbers a and b such that:
a*b = 6 and a+b = 7
We find that there are no integer or easily identifiable decimal numbers that meet this criteria.

Using the quadratic equation for the general equation to find the real roots
am²+bm+c=0
(-b ± √(b²-4ac)) / (2a)
and the coefficients of your formula a=1, b=6 and c=7
-6±√(36-(4)(1)(7)) / (2)(1)
(-6±√(36 - 28) ) / 2
-3 + √8 / √4 = -3 + √2
-3 - √8 / √4 = -3 - √2

m = -3+√2 or m = -3 - √2

Answer 3

m^2+6m+7=0
take 1/2 of 6 and square it = 9
(m^2+6m+9)+7-9=0
(m+3)^2 - 2=0

Answer 4

m^2 = -6m - 7
Note that you must move the right hand stuff to the left side
m^2+6m+7=0
Then you can get your solutions.