How do you solve #m^ { 2} - 4m - 16= - 4#?

1 Answer
naomibeth
Mar 21, 2018

#m = 6, -2#

Explanation:

Since it is a quadratic equation, we must make sure it is set equal to zero.

Therefore, we add 4 to both sides:
#m^2-4m-16 = -4#
#m^2-4m-12 = 0#

Now that our equation is set equal to 0, we have a couple of options. We can try to factor it, complete the square, or use the quadratic formula. It is easier to factor if you can, so always check if you can factor first.

In this case, the equation is factorable (Lucky us)! If we take the equation and begin to factor, we get:
#(m-6)(m+2) = 0#

(If you would like an explanation of how I factored this, just let me know)

After this, we use the Zero Product Property to solve for m. We separate the factors and set them each equal to 0.

#(m-6 )= 0#
#(m+2 )= 0#

Then, we can solve each for m.

#(m-6) = 0#
#m = 6#

and

#(m+2) = 0#
#m=-2#

Therefore, our solutions/zeros of the equation are #6# and #-2# (#m = 6, -2#).

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