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Algebra/Finding real solutions for an equation

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Expert: - 2/15/2011


Question
Find all real solutions of the equation .

(x-2)^2=16

Can you explain the steps to solve this equation?

Answer
It is known that if t^2 = 16, t = -4 or t = 4.
Since t = x-2, the equations to solve are x - 2 = -4 and x - 2 = 4.

Adding 2 to both sides in the 1st equation gives x = -2.
Adding 2 to both sides in the 2nd equation gives x = 6.

Testing both of these number, (-2-2)^2 = (-4)^2 = 16 and (6-2)^2 = 4^2 = 16.

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