3k^2+73=33k

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Solution for 3k^2+73=33k equation:


Simplifying
3k2 + 73 = 33k

Reorder the terms:
73 + 3k2 = 33k

Solving
73 + 3k2 = 33k

Solving for variable 'k'.

Reorder the terms:
73 + -33k + 3k2 = 33k + -33k

Combine like terms: 33k + -33k = 0
73 + -33k + 3k2 = 0

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

Divide each side by '3'.
24.33333333 + -11k + k2 = 0

Move the constant term to the right:

Add '-24.33333333' to each side of the equation.
24.33333333 + -11k + -24.33333333 + k2 = 0 + -24.33333333

Reorder the terms:
24.33333333 + -24.33333333 + -11k + k2 = 0 + -24.33333333

Combine like terms: 24.33333333 + -24.33333333 = 0.00000000
0.00000000 + -11k + k2 = 0 + -24.33333333
-11k + k2 = 0 + -24.33333333

Combine like terms: 0 + -24.33333333 = -24.33333333
-11k + k2 = -24.33333333

The k term is -11k.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11k + 30.25 + k2 = -24.33333333 + 30.25

Reorder the terms:
30.25 + -11k + k2 = -24.33333333 + 30.25

Combine like terms: -24.33333333 + 30.25 = 5.91666667
30.25 + -11k + k2 = 5.91666667

Factor a perfect square on the left side:
(k + -5.5)(k + -5.5) = 5.91666667

Calculate the square root of the right side: 2.432419921

Break this problem into two subproblems by setting 
(k + -5.5) equal to 2.432419921 and -2.432419921.

Subproblem 1

k + -5.5 = 2.432419921 Simplifying k + -5.5 = 2.432419921 Reorder the terms: -5.5 + k = 2.432419921 Solving -5.5 + k = 2.432419921 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + k = 2.432419921 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + k = 2.432419921 + 5.5 k = 2.432419921 + 5.5 Combine like terms: 2.432419921 + 5.5 = 7.932419921 k = 7.932419921 Simplifying k = 7.932419921

Subproblem 2

k + -5.5 = -2.432419921 Simplifying k + -5.5 = -2.432419921 Reorder the terms: -5.5 + k = -2.432419921 Solving -5.5 + k = -2.432419921 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + k = -2.432419921 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + k = -2.432419921 + 5.5 k = -2.432419921 + 5.5 Combine like terms: -2.432419921 + 5.5 = 3.067580079 k = 3.067580079 Simplifying k = 3.067580079

Solution

The solution to the problem is based on the solutions from the subproblems. k = {7.932419921, 3.067580079}

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