How do you find the root of the equation by completing the square m2-6m-7 equals 0?

Answer 1

You need to find two numbers that multiplied together give -7 (e.g. 7 and -1, or -7 and 1)

AND you have to get these to add up to -6 (and the only pair that do this is -7+1

So to factorise the equation (i.e. find the roots)

==> (m - 7)(m + 1) = 0

==> m - 7 = 0 and m + 1 = 0

==> m = 7, -1

Answer 2

First, you must determine the constant part (without variables) for the left side of the equation. To get this, you calculate 1/2 of 6, and square the answer - so, 3 squared, which equals 9.To get +9 on the left side (instead of -7), you need to add 16 to each side. The result is:

m2 - 6m + 9 = 16

Now, you have a perfect square on the left (it's the square of m - 3), so you can write this as:

(m - 3) squared = 16

Now you take the square root:

m - 3 = (plus-or-minus) 4

You solve the two equations (one for +4, one for -4).