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 + x + -1 = 0

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

Solving
-1 + x + 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 + x + 1 + x2 = 0 + 1

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

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

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

The x term is x.  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.
x + 0.25 + x2 = 1 + 0.25

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

Combine like terms: 1 + 0.25 = 1.25
0.25 + x + 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 = 0.618033989 x = 0.618033989 Simplifying x = 0.618033989

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 = -1.618033989 x = -1.618033989 Simplifying x = -1.618033989

Solution

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

See similar equations:

| (4a+3)(y+3)=0 | | 3wsquared+22w+7=0 | | -42=7+7x | | -x-7=-42+6x | | -2x^2-28x+98=0 | | 25=v+12 | | 3.5*x=18 | | 7/3*.3= | | -6x-9=79+2x | | (6-z)(4z-5)=0 | | 4sin^2x-4=0 | | 3f+4.3= | | 5(10x-17)=365 | | -3/4=5/7w-3/2 | | 12d-10=8d+16 | | 6x+5+10x-1+6x+5+8x+9+8x+9=360 | | -12x-49=-9x+23 | | 3w-6=-5 | | .25q+.10d=2.75 | | (x^3)-3.5*(x^2)-40=0 | | 4(x-5)+2x=2x-8 | | t^2-7t-10=0 | | 0.1/x=1.1/100 | | 26-1/4 | | -x-91=-6x+24 | | (20x+5)=(24x+5) | | 4x^2-24x=36 | | 5(2m+3)-(1-2m)=2[2(3+2m)-(3-m)] | | w(40+w)=6000 | | 5x^2-12x+10=x^2+10x | | 3x-25=9x+53 | | 5x+13-10=0 |

Equations solver categories