What is the answer to sqrt(x^2-2x+1)=1-x ?

The answer to sqrt(x^2-2x+1)=1-x is x<= 1

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

x^{2} - 2 x + 1 = 1 - x

x \leq 1

Solution steps

x^{2} - 2 x + 1 = 1 - x

Square both sides:

x^{2} - 2 x + 1 = 1 - 2 x + x^{2}

x^{2} - 2 x + 1 = 1 - 2 x + x^{2}

Solve

x^{2} - 2 x + 1 = 1 - 2 x + x^{2} :

True for all

x

True for all x

Verify Solutions:

x < 1

True

, x = 1

True

, x > 1

False

The solution is

x \leq 1

6 x + x - 1 = 0

- 12 x^{2} + 2 x = 0

x - 10 = x - 10

k + 2 + k - 2 = 3

What is the answer to sqrt(x^2-2x+1)=1-x ?
The answer to sqrt(x^2-2x+1)=1-x is x<= 1
Solve for x: sqrt(x^2-2x+1)=1-x
The solution is x<= 1