5k^2=60-2k

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Solution for 5k^2=60-2k equation:


Simplifying
5k2 = 60 + -2k

Solving
5k2 = 60 + -2k

Solving for variable 'k'.

Reorder the terms:
-60 + 2k + 5k2 = 60 + -2k + -60 + 2k

Reorder the terms:
-60 + 2k + 5k2 = 60 + -60 + -2k + 2k

Combine like terms: 60 + -60 = 0
-60 + 2k + 5k2 = 0 + -2k + 2k
-60 + 2k + 5k2 = -2k + 2k

Combine like terms: -2k + 2k = 0
-60 + 2k + 5k2 = 0

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

Divide each side by '5'.
-12 + 0.4k + k2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 0.4k + 12 + k2 = 0 + 12

Reorder the terms:
-12 + 12 + 0.4k + k2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 0.4k + k2 = 0 + 12
0.4k + k2 = 0 + 12

Combine like terms: 0 + 12 = 12
0.4k + k2 = 12

The k term is 0.4k.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4k + 0.04 + k2 = 12 + 0.04

Reorder the terms:
0.04 + 0.4k + k2 = 12 + 0.04

Combine like terms: 12 + 0.04 = 12.04
0.04 + 0.4k + k2 = 12.04

Factor a perfect square on the left side:
(k + 0.2)(k + 0.2) = 12.04

Calculate the square root of the right side: 3.469870315

Break this problem into two subproblems by setting 
(k + 0.2) equal to 3.469870315 and -3.469870315.

Subproblem 1

k + 0.2 = 3.469870315 Simplifying k + 0.2 = 3.469870315 Reorder the terms: 0.2 + k = 3.469870315 Solving 0.2 + k = 3.469870315 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + k = 3.469870315 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + k = 3.469870315 + -0.2 k = 3.469870315 + -0.2 Combine like terms: 3.469870315 + -0.2 = 3.269870315 k = 3.269870315 Simplifying k = 3.269870315

Subproblem 2

k + 0.2 = -3.469870315 Simplifying k + 0.2 = -3.469870315 Reorder the terms: 0.2 + k = -3.469870315 Solving 0.2 + k = -3.469870315 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + k = -3.469870315 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + k = -3.469870315 + -0.2 k = -3.469870315 + -0.2 Combine like terms: -3.469870315 + -0.2 = -3.669870315 k = -3.669870315 Simplifying k = -3.669870315

Solution

The solution to the problem is based on the solutions from the subproblems. k = {3.269870315, -3.669870315}

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