x^2-x-1=

Simple and best practice solution for x^2-x-1= equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for x^2-x-1= equation:


Simplifying
x2 + -1x + -1 = 0

Reorder the terms:
-1 + -1x + x2 = 0

Solving
-1 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x + x2 = 0 + 1
-1x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1x + x2 = 1

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1x + x2 = 1.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -0.5 = 1.118033989 Simplifying x + -0.5 = 1.118033989 Reorder the terms: -0.5 + x = 1.118033989 Solving -0.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.118033989 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.118033989 + 0.5 x = 1.118033989 + 0.5 Combine like terms: 1.118033989 + 0.5 = 1.618033989 x = 1.618033989 Simplifying x = 1.618033989

Subproblem 2

x + -0.5 = -1.118033989 Simplifying x + -0.5 = -1.118033989 Reorder the terms: -0.5 + x = -1.118033989 Solving -0.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.118033989 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.118033989 + 0.5 x = -1.118033989 + 0.5 Combine like terms: -1.118033989 + 0.5 = -0.618033989 x = -0.618033989 Simplifying x = -0.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.618033989, -0.618033989}

See similar equations:

| 1x-8+2x=6x-10 | | 101.0=(X/100000)*100 | | 8y=6y-8 | | 24(cos)X=-12 | | 7m-12whenm=3 | | 24cosx=-12 | | -41+17=-5+13 | | 95.4=(X/50000)*100 | | 3m^2+m-3= | | Log(x)256=4 | | 6x+2y-z=0 | | 6x-2x+8=x+6 | | 3x+7=41-5x | | 0.5n=7.5 | | 3n^2-n-1= | | 10c=cm | | -3(x+4)+6=7(x+4)+4 | | 10c= | | 50=4x+8 | | 2a^2+a-5= | | p^2+2p+1= | | guilen+40=9 | | 2.4-.24(5-2x)=0 | | (4-n)/(2n-8) | | 9y+7+2y= | | =11.4*2*3.1415926 | | -4+3x=-12x+17x | | 7.8j-5.8j=7.6 | | (3/5x)-(8/15)=4 | | 2*3.1415926*3.7= | | 3x-2=1+5x | | 7y+1=16-3y |

Equations solver categories