SOLUTION: Is this problem solveable? Xsquared + X = 1 I have tried (x+1)(x)=1 (-X-1)(-X)=1 Xsquared = 1-x Thanks

Algebra ->  Equations -> SOLUTION: Is this problem solveable? Xsquared + X = 1 I have tried (x+1)(x)=1 (-X-1)(-X)=1 Xsquared = 1-x Thanks      Log On


   

Question 51894: Is this problem solveable? Xsquared + X = 1
I have tried (x+1)(x)=1
(-X-1)(-X)=1
Xsquared = 1-x
Thanks
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
I will give you TWO solutions:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=0.618033988749895,x=-1.61803398874989.
  • Graphical form: Equation x%5E2%2Bx=1 was fully solved.
  • Text form: x^2+x=1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%5E2%2Bx=1+%29
    For tutors: simplify_cartoon( x^2+x=1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%5E2%2Bx=highlight_red%28+1+%29.
Moved these terms to the left highlight_green%28+-1+%29
It becomes x%5E2%2Bx-highlight_green%28+1+%29=0.
Look at highlight_red%28+x%5E2%2Bx-1+%29=0.
Equation highlight_red%28+x%5E2%2Bx-1=0+%29 is a quadratic equation: x^2+x-1 =0, and has solutions 0.618033988749895,-1.61803398874989
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=0.618033988749895,x=-1.61803398874989.

Universal Simplifier and Solver


Done!


Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A-1=5.

Discriminant d=5 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+5+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+5+%29%29%2F2%5C1+=+0.618033988749895
x%5B2%5D+=+%28-%281%29-sqrt%28+5+%29%29%2F2%5C1+=+-1.61803398874989

Quadratic expression 1x%5E2%2B1x%2B-1 can be factored:
1x%5E2%2B1x%2B-1+=+1%28x-0.618033988749895%29%2A%28x--1.61803398874989%29
Again, the answer is: 0.618033988749895, -1.61803398874989. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-1+%29