k^2-k+-1=0

Simple and best practice solution for k^2-k+-1=0 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 k^2-k+-1=0 equation:


Simplifying
k2 + -1k + -1 = 0

Reorder the terms:
-1 + -1k + k2 = 0

Solving
-1 + -1k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + -1k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1k + k2 = 0 + 1
-1k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1k + k2 = 1

The k term is -1k.  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.
-1k + 0.25 + k2 = 1 + 0.25

Reorder the terms:
0.25 + -1k + k2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1k + k2 = 1.25

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

Calculate the square root of the right side: 1.118033989

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

Subproblem 1

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

Subproblem 2

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

Solution

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

See similar equations:

| x^2+8x+10= | | 2x^2-4x= | | 11x-2= | | -5(-2t-4)= | | 7+8x= | | -1(-c+100)= | | 3(2-1+3)+x=12 | | 3x-2y-12=0 | | X-4(2x)=-6 | | 5x-45x^2=0 | | 15n-308=5n-8 | | -11(4y+2)= | | 18x^2+33x+14=0 | | -4d-3(d+8)=10 | | 4a+6=7A-10 | | 4w+12=6w-26 | | 1x-41=9 | | 127-7x=38x+17 | | -3(-x-5)= | | Y=4x+c | | 4x-2x=0 | | -7(-v+4)= | | x^5=4 | | 2[x+5(6-x)+16]-10=50-10x | | 4x*x-33x+33=-9x+6 | | 2x-6+3x-4=30 | | -6(-5t-2)= | | 0.2=2.4 | | 2x^2+7x-60=0 | | W+30=11w | | 6x*x-23x-4=0 | | 7p-(3p+4)=-(2p-1)+10 |

Equations solver categories