x^{2}+x-1=0

Question

x^{2}+x-1=0

Accepted Answer

Step:1 ：The given equation is a quadratic equation in the form (ax^{2}+bx+c=0), where (a=1), (b=1), and (c=-1).Step:2 ：The solutions to a quadratic equation can be found using the quadratic formula: (x=frac{-bpmsqrt{b^{2}-4ac}}{2a}).Step:3 ：Substituting the values of (a), (b), and (c) into the quadratic formula, we get two solutions: (x1 = 0.6180339887498949) and (x2 = -1.618033988749895).Step:4 ：In exact form, the solutions are (x=frac{-1+sqrt{5}}{2}) and (x=frac{-1-sqrt{5}}{2}).Step:5 ：Final Answer: The solutions to the equation (x^{2}+x-1=0) are (xapprox0.618) and (xapprox-1.618). Therefore, the solutions are (boxed{x=frac{-1+sqrt{5}}{2}, x=frac{-1-sqrt{5}}{2}}).

Answer

Step: 1 ：The given equation is a quadratic equation in the form (ax^{2}+bx+c=0), where (a=1), (b=1), and (c=-1).Step: 2 ：The solutions to a quadratic equation can be found using the quadratic formula: (x=frac{-bpmsqrt{b^{2}-4ac}}{2a}).Step: 3 ：Substituting the values of (a), (b), and (c) into the quadratic formula, we get two solutions: (x1 = 0.6180339887498949) and (x2 = -1.618033988749895).Step: 4 ：In exact form, the solutions are (x=frac{-1+sqrt{5}}{2}) and (x=frac{-1-sqrt{5}}{2}).Step: 5 ：Final Answer: The solutions to the equation (x^{2}+x-1=0) are (xapprox0.618) and (xapprox-1.618). Therefore, the solutions are (boxed{x=frac{-1+sqrt{5}}{2}, x=frac{-1-sqrt{5}}{2}}).

$x^{2} + x - 1 = 0$

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Popular Problems

x2+x−1=0

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Popular Problems

$x^{2} + x - 1 = 0$