SOLUTION: Dear Math Tutor, Please help me with: 2 times the square root of x-1 + 1 = x 2 times the square root of x-1 = x-1 (2 times the square root of x-1)^2 = (x-1)^2 4(x-1) = x^2-2

Algebra ->  Real-numbers -> SOLUTION: Dear Math Tutor, Please help me with: 2 times the square root of x-1 + 1 = x 2 times the square root of x-1 = x-1 (2 times the square root of x-1)^2 = (x-1)^2 4(x-1) = x^2-2      Log On


   

Question 873961: Dear Math Tutor,
Please help me with:
2 times the square root of x-1 + 1 = x
2 times the square root of x-1 = x-1
(2 times the square root of x-1)^2 = (x-1)^2
4(x-1) = x^2-2x+1
My frustration: Why is there an extra 2x on the right hand side now? Shouldn't it just be x^2+1? Where did 2x come from? Am I missing a rule?
With gratitude,
Nats
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The reason for the 2x comes from expanding out (x-1)^2

When you expand out (x-1)^2, you will NOT get x^2 + 1

That's a very common fallacy people fall for.

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Here is what you should get

(x-1)^2 = (x-1)*(x-1)

(x-1)^2 = x(x-1) - 1(x-1)

(x-1)^2 = x^2 - x - x + 1

(x-1)^2 = x^2 - 2x + 1

I recommend using a rectangle to help multiply (example of what I mean shown below. In the example, they are multiplying out %28x%2B3%29%28x-2%29)


(Image Source: http://www.shelovesmath.com/algebra/intermediate-algebra/introduction-to-polynomials/)