SOLUTION: for function f(x)=x^2-2x+1,solve f(x)=0 I'm really lost with this one! Your help would be greatly appreciated =)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: for function f(x)=x^2-2x+1,solve f(x)=0 I'm really lost with this one! Your help would be greatly appreciated =)      Log On


   

Question 297338: for function f(x)=x^2-2x+1,solve f(x)=0 I'm really lost with this one! Your help would be greatly appreciated =)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=x%5E2-2x%2B1 Start with the given function.


0=x%5E2-2x%2B1 Plug in f%28x%29=0


x%5E2-2x%2B1=0 Rearrange the equation.


Notice that the quadratic x%5E2-2x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-2, and C=1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=1


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%281%29%281%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4-4+%29%29%2F%282%281%29%29 Multiply 4%281%29%281%29 to get 4


x+=+%282+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 4 from 4 to get 0


x+=+%282+%2B-+sqrt%28+0+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+0%29%2F%282%29 Take the square root of 0 to get 0.


x+=+%282+%2B+0%29%2F%282%29 or x+=+%282+-+0%29%2F%282%29 Break up the expression.


x+=+%282%29%2F%282%29 or x+=++%282%29%2F%282%29 Combine like terms.


x+=+1 or x+=+1 Simplify.


So the only solution is x+=+1