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Write x^2-2x-3=0 in the form (x-a)^2=b, where a and b are integers

Karen Wright

in Mathematics

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Ashley Howard on October 21, 2018

This is written in a way meant to throw you, I think, but all it's asking you to do is to complete the square! it will give you the square of a binomial on the left, below, its remains of a whole number, to the right (b).x2 - 2x - 3 = 0 ... add 3 to both sidesx2 - 2x + __ = 3 ... the empty space is where you need to complete the square. this is done by dividing the "half" coefficient (-2) 2, then squaring it. -2/2 is -1 ... -12 is 1. therefore:x2 - 2x + 1 = 3 + 1you have to balance it by adding 1 to both sides. what you do to one side you must do to the other. the next step is to factor the left side:(x - 1)(x - 1) = 4 rewrite it as (x - 1)2 = 4 ... this is your answer.


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