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Question 1065648: If 2 times a number is decreased by 6, the principal square root of this difference is 7 less than the number. Find the number(s).
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! number is x
2x-6 is the number whose square root is x-7
square both sides
2x-6=(x-7)^2=x^2-14x+49
0=x^2-16x+55
0=(x-11)(x-5)
x=11 or 5
if 11, square root of 16 is 4, 7 fewer than 11.
if 5, square root of 4 is 2, and that is not 7 fewer than 5, and that is the principal square root.
11 is the number.
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