k+k(k-45)+(k-45)+(k-45)=

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Solution for k+k(k-45)+(k-45)+(k-45)= equation: 


Simplifying
k + k(k + -45) + (k + -45) + (k + -45) = 0

Reorder the terms:
k + k(-45 + k) + (k + -45) + (k + -45) = 0
k + (-45 * k + k * k) + (k + -45) + (k + -45) = 0
k + (-45k + k2) + (k + -45) + (k + -45) = 0

Reorder the terms:
k + -45k + k2 + (-45 + k) + (k + -45) = 0

Remove parenthesis around (-45 + k)
k + -45k + k2 + -45 + k + (k + -45) = 0

Reorder the terms:
k + -45k + k2 + -45 + k + (-45 + k) = 0

Remove parenthesis around (-45 + k)
k + -45k + k2 + -45 + k + -45 + k = 0

Reorder the terms:
-45 + -45 + k + -45k + k + k + k2 = 0

Combine like terms: -45 + -45 = -90
-90 + k + -45k + k + k + k2 = 0

Combine like terms: k + -45k = -44k
-90 + -44k + k + k + k2 = 0

Combine like terms: -44k + k = -43k
-90 + -43k + k + k2 = 0

Combine like terms: -43k + k = -42k
-90 + -42k + k2 = 0

Solving
-90 + -42k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -42k + 90 + k2 = 0 + 90

Reorder the terms:
-90 + 90 + -42k + k2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -42k + k2 = 0 + 90
-42k + k2 = 0 + 90

Combine like terms: 0 + 90 = 90
-42k + k2 = 90

The k term is -42k.  Take half its coefficient (-21).
Square it (441) and add it to both sides.

Add '441' to each side of the equation.
-42k + 441 + k2 = 90 + 441

Reorder the terms:
441 + -42k + k2 = 90 + 441

Combine like terms: 90 + 441 = 531
441 + -42k + k2 = 531

Factor a perfect square on the left side:
(k + -21)(k + -21) = 531

Calculate the square root of the right side: 23.043437244

Break this problem into two subproblems by setting 
(k + -21) equal to 23.043437244 and -23.043437244.


Subproblem 1
k + -21 = 23.043437244

Simplifying
k + -21 = 23.043437244

Reorder the terms:
-21 + k = 23.043437244

Solving
-21 + k = 23.043437244

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '21' to each side of the equation.
-21 + 21 + k = 23.043437244 + 21

Combine like terms: -21 + 21 = 0
0 + k = 23.043437244 + 21
k = 23.043437244 + 21

Combine like terms: 23.043437244 + 21 = 44.043437244
k = 44.043437244

Simplifying
k = 44.043437244


Subproblem 2
k + -21 = -23.043437244

Simplifying
k + -21 = -23.043437244

Reorder the terms:
-21 + k = -23.043437244

Solving
-21 + k = -23.043437244

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '21' to each side of the equation.
-21 + 21 + k = -23.043437244 + 21

Combine like terms: -21 + 21 = 0
0 + k = -23.043437244 + 21
k = -23.043437244 + 21

Combine like terms: -23.043437244 + 21 = -2.043437244
k = -2.043437244

Simplifying
k = -2.043437244


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {44.043437244, -2.043437244}

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