k^2+20k-46=0

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Solution for k^2+20k-46=0 equation: 


Simplifying
k2 + 20k + -46 = 0

Reorder the terms:
-46 + 20k + k2 = 0

Solving
-46 + 20k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 20k + 46 + k2 = 0 + 46

Reorder the terms:
-46 + 46 + 20k + k2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 20k + k2 = 0 + 46
20k + k2 = 0 + 46

Combine like terms: 0 + 46 = 46
20k + k2 = 46

The k term is 20k.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20k + 100 + k2 = 46 + 100

Reorder the terms:
100 + 20k + k2 = 46 + 100

Combine like terms: 46 + 100 = 146
100 + 20k + k2 = 146

Factor a perfect square on the left side:
(k + 10)(k + 10) = 146

Calculate the square root of the right side: 12.083045974

Break this problem into two subproblems by setting 
(k + 10) equal to 12.083045974 and -12.083045974.


Subproblem 1
k + 10 = 12.083045974

Simplifying
k + 10 = 12.083045974

Reorder the terms:
10 + k = 12.083045974

Solving
10 + k = 12.083045974

Solving for variable 'k'.

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

Add '-10' to each side of the equation.
10 + -10 + k = 12.083045974 + -10

Combine like terms: 10 + -10 = 0
0 + k = 12.083045974 + -10
k = 12.083045974 + -10

Combine like terms: 12.083045974 + -10 = 2.083045974
k = 2.083045974

Simplifying
k = 2.083045974


Subproblem 2
k + 10 = -12.083045974

Simplifying
k + 10 = -12.083045974

Reorder the terms:
10 + k = -12.083045974

Solving
10 + k = -12.083045974

Solving for variable 'k'.

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

Add '-10' to each side of the equation.
10 + -10 + k = -12.083045974 + -10

Combine like terms: 10 + -10 = 0
0 + k = -12.083045974 + -10
k = -12.083045974 + -10

Combine like terms: -12.083045974 + -10 = -22.083045974
k = -22.083045974

Simplifying
k = -22.083045974


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {2.083045974, -22.083045974}

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