Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 150813: I'm confused with this function problem.
It states: For the function f(x) = x^2-2x+1 solve f(x) = 0.
I'm confused about this question, please help me. Thank you.: I'm confused with this function problem.
It states: For the function f(x) = x^2-2x+1 solve f(x) = 0.
I'm confused about this question, please help me. Thank you.
Answer by jim_thompson5910(9166) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^2-2x+1 Start with the given function


0= x^2-2x+1 Plug in f(x)=0


Here are two ways to solve for x:


Method # 1 Factoring:


x^2-2x+1=0 Start with the given equation


(x-1)(x-1)=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-1=0 or x-1=0

x=1 or x=1 Now solve for x in each case


Since we have a repeating answer, our only answer is x=1


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Method # 2 Quadratic Formula:


x^2-2x+1=0 Start with the given equation.


From x^2-2x+1, we can see that a=1, b=-2, and c=1


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(-2) +- sqrt( (-2)^2-4(1)(1) ))/(2(1)) Plug in a=1, b=-2, and c=1


x = (2 +- sqrt( (-2)^2-4(1)(1) ))/(2(1)) Negate -2 to get 2.


x = (2 +- sqrt( 4-4(1)(1) ))/(2(1)) Square -2 to get 4.


x = (2 +- sqrt( 4-4 ))/(2(1)) Multiply 4(1)(1) to get 4


x = (2 +- sqrt( 0 ))/(2(1)) Subtract 4 from 4 to get 0


x = (2 +- sqrt( 0 ))/(2) Multiply 2 and 1 to get 2.


x = (2 +- 0)/(2) Take the square root of 0 to get 0.


x = (2 + 0)/(2) or x = (2 - 0)/(2) Break up the expression.


x = (2)/(2) or x = (2)/(2) Combine like terms.


x = 1 or x = 1 Simplify.


So the solution is x = 1

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Answer:


Using either method, we get the solution x = 1