k^2-k=3

Simple and best practice solution for k^2-k=3 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=3 equation:


Simplifying
k2 + -1k = 3

Reorder the terms:
-1k + k2 = 3

Solving
-1k + k2 = 3

Solving for variable 'k'.

Reorder the terms:
-3 + -1k + k2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -1k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1k + 3 + k2 = 0 + 3

Reorder the terms:
-3 + 3 + -1k + k2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1k + k2 = 0 + 3
-1k + k2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1k + k2 = 3

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 = 3 + 0.25

Reorder the terms:
0.25 + -1k + k2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1k + k2 = 3.25

Factor a perfect square on the left side:
(k + -0.5)(k + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(k + -0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

k + -0.5 = 1.802775638 Simplifying k + -0.5 = 1.802775638 Reorder the terms: -0.5 + k = 1.802775638 Solving -0.5 + k = 1.802775638 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 = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + k = 1.802775638 + 0.5 k = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 k = 2.302775638 Simplifying k = 2.302775638

Subproblem 2

k + -0.5 = -1.802775638 Simplifying k + -0.5 = -1.802775638 Reorder the terms: -0.5 + k = -1.802775638 Solving -0.5 + k = -1.802775638 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 = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + k = -1.802775638 + 0.5 k = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 k = -1.302775638 Simplifying k = -1.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.302775638, -1.302775638}

See similar equations:

| 2(2x-7)+2x=28 | | x^20-2x^10=8 | | n^3+6n^2+11n+9=0 | | -6x+9y=-12 | | x^3-8x+6x=3 | | 7+-4(d-3)=23 | | 7+-4(d-3)=-3 | | 20-2a=7a+2 | | 4a+-2(a+9)=6 | | 12x-8=9x+52 | | -4x-15=-79 | | 4(x-9)=3(x+7) | | 2(3x-5)=26 | | 2(3x-5)=33 | | 12a+19=13a-15 | | 8-2x+(8x-4)-(2x+5)=-3[2x-3(4x+5)+(x+3)]+9 | | 48-3a=30 | | 57+7a=57 | | 2+6*(16-8)= | | 10b+36b+24b=525 | | 4x^4+36x^2=-81 | | (2y+7)+(3y-17)=180 | | (x+56)+(2x-2)=180 | | 2x^3(2x^2-9x+2)= | | X+2x+(2x+3)=48 | | (x+56)+(2y+7)=180 | | 3x^4-18x^3-80x^2-6x-27=0 | | 20x-5=19x+5 | | 10-7x=10x-9x-22 | | 25m^2+42=65m | | 10a^2-13a-22=8 | | (3y-8)(-7y^2+7y+3)= |

Equations solver categories