Question 150813
{{{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 <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




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}}}