4k(k+10)=10

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Solution for 4k(k+10)=10 equation: 


Simplifying
4k(k + 10) = 10

Reorder the terms:
4k(10 + k) = 10
(10 * 4k + k * 4k) = 10
(40k + 4k2) = 10

Solving
40k + 4k2 = 10

Solving for variable 'k'.

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

Combine like terms: 10 + -10 = 0
-10 + 40k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 20k + 2k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 20k + 2k2)' equal to zero and attempt to solve:

Simplifying
-5 + 20k + 2k2 = 0

Solving
-5 + 20k + 2k2 = 0

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

Divide each side by '2'.
-2.5 + 10k + k2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 10k + 2.5 + k2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 10k + k2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 10k + k2 = 0 + 2.5
10k + k2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
10k + k2 = 2.5

The k term is 10k.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10k + 25 + k2 = 2.5 + 25

Reorder the terms:
25 + 10k + k2 = 2.5 + 25

Combine like terms: 2.5 + 25 = 27.5
25 + 10k + k2 = 27.5

Factor a perfect square on the left side:
(k + 5)(k + 5) = 27.5

Calculate the square root of the right side: 5.244044241

Break this problem into two subproblems by setting 
(k + 5) equal to 5.244044241 and -5.244044241.


Subproblem 1
k + 5 = 5.244044241

Simplifying
k + 5 = 5.244044241

Reorder the terms:
5 + k = 5.244044241

Solving
5 + k = 5.244044241

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + -5 + k = 5.244044241 + -5

Combine like terms: 5 + -5 = 0
0 + k = 5.244044241 + -5
k = 5.244044241 + -5

Combine like terms: 5.244044241 + -5 = 0.244044241
k = 0.244044241

Simplifying
k = 0.244044241


Subproblem 2
k + 5 = -5.244044241

Simplifying
k + 5 = -5.244044241

Reorder the terms:
5 + k = -5.244044241

Solving
5 + k = -5.244044241

Solving for variable 'k'.

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

Add '-5' to each side of the equation.
5 + -5 + k = -5.244044241 + -5

Combine like terms: 5 + -5 = 0
0 + k = -5.244044241 + -5
k = -5.244044241 + -5

Combine like terms: -5.244044241 + -5 = -10.244044241
k = -10.244044241

Simplifying
k = -10.244044241


Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.244044241, -10.244044241}
Solution
k = {0.244044241, -10.244044241}

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