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

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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)   (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 was fully solved.
  • Text form: x^2+x=1 simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x^2+x=1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved these terms to the left highlight_green%28+-1+%29
It becomes .
Look at .
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 .
Result:
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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=5 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.618033988749895, -1.61803398874989. Here's your graph:
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