10k^2+20k-40=4

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Solution for 10k^2+20k-40=4 equation: 


Simplifying
10k2 + 20k + -40 = 4

Reorder the terms:
-40 + 20k + 10k2 = 4

Solving
-40 + 20k + 10k2 = 4

Solving for variable 'k'.

Reorder the terms:
-40 + -4 + 20k + 10k2 = 4 + -4

Combine like terms: -40 + -4 = -44
-44 + 20k + 10k2 = 4 + -4

Combine like terms: 4 + -4 = 0
-44 + 20k + 10k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + 10k + 5k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-22 + 10k + 5k2)' equal to zero and attempt to solve:

Simplifying
-22 + 10k + 5k2 = 0

Solving
-22 + 10k + 5k2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-4.4 + 2k + k2 = 0

Move the constant term to the right:

Add '4.4' to each side of the equation.
-4.4 + 2k + 4.4 + k2 = 0 + 4.4

Reorder the terms:
-4.4 + 4.4 + 2k + k2 = 0 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + 2k + k2 = 0 + 4.4
2k + k2 = 0 + 4.4

Combine like terms: 0 + 4.4 = 4.4
2k + k2 = 4.4

The k term is 2k.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2k + 1 + k2 = 4.4 + 1

Reorder the terms:
1 + 2k + k2 = 4.4 + 1

Combine like terms: 4.4 + 1 = 5.4
1 + 2k + k2 = 5.4

Factor a perfect square on the left side:
(k + 1)(k + 1) = 5.4

Calculate the square root of the right side: 2.323790008

Break this problem into two subproblems by setting 
(k + 1) equal to 2.323790008 and -2.323790008.


Subproblem 1
k + 1 = 2.323790008

Simplifying
k + 1 = 2.323790008

Reorder the terms:
1 + k = 2.323790008

Solving
1 + k = 2.323790008

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = 2.323790008 + -1

Combine like terms: 1 + -1 = 0
0 + k = 2.323790008 + -1
k = 2.323790008 + -1

Combine like terms: 2.323790008 + -1 = 1.323790008
k = 1.323790008

Simplifying
k = 1.323790008


Subproblem 2
k + 1 = -2.323790008

Simplifying
k + 1 = -2.323790008

Reorder the terms:
1 + k = -2.323790008

Solving
1 + k = -2.323790008

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1 + k = -2.323790008 + -1

Combine like terms: 1 + -1 = 0
0 + k = -2.323790008 + -1
k = -2.323790008 + -1

Combine like terms: -2.323790008 + -1 = -3.323790008
k = -3.323790008

Simplifying
k = -3.323790008


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {1.323790008, -3.323790008}
Solution
k = {1.323790008, -3.323790008}

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