k^2+k=100-20k

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Solution for k^2+k=100-20k equation:


Simplifying
k2 + k = 100 + -20k

Reorder the terms:
k + k2 = 100 + -20k

Solving
k + k2 = 100 + -20k

Solving for variable 'k'.

Reorder the terms:
-100 + k + 20k + k2 = 100 + -20k + -100 + 20k

Combine like terms: k + 20k = 21k
-100 + 21k + k2 = 100 + -20k + -100 + 20k

Reorder the terms:
-100 + 21k + k2 = 100 + -100 + -20k + 20k

Combine like terms: 100 + -100 = 0
-100 + 21k + k2 = 0 + -20k + 20k
-100 + 21k + k2 = -20k + 20k

Combine like terms: -20k + 20k = 0
-100 + 21k + k2 = 0

Factor a trinomial.
(-25 + -1k)(4 + -1k) = 0


Subproblem 1
Set the factor '(-25 + -1k)' equal to zero and attempt to solve:

Simplifying
-25 + -1k = 0

Solving
-25 + -1k = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1k = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1k = 0 + 25
-1k = 0 + 25

Combine like terms: 0 + 25 = 25
-1k = 25

Divide each side by '-1'.
k = -25

Simplifying
k = -25

Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-25, 4}

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