How do you solve #x^ { 2} - 2x = 99#?

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Answer 1 · 2016-11-29T19:03:24

#x = 11# and #x = -9#

First create a quadratic equation by subtracting #99# from each side of the equation:
#x^2 - 2x - 99 = 99 - 99#

#x^2 - 2x - 99 = 0#

Now playing with pairs of multiples for #99# such as (1,99) and (3,33) and (9,11) you factor the quadratic to:

#(x - 11)(x + 9) = 0#

Now solve for #x - 11# and #x + 9# equal to #0#:

#x - 11 = 0#

#x - 11 + 11 = 0 + 11#

#x = 11#

and

#x + 9 = 0#

#x + 9 - 9 = 0 - 9#

#x = -9#