3k^2-21k+10=0

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Solution for 3k^2-21k+10=0 equation:


Simplifying
3k2 + -21k + 10 = 0

Reorder the terms:
10 + -21k + 3k2 = 0

Solving
10 + -21k + 3k2 = 0

Solving for variable 'k'.

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

Divide each side by '3'.
3.333333333 + -7k + k2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -7k + -3.333333333 + k2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -7k + k2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -7k + k2 = 0 + -3.333333333
-7k + k2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-7k + k2 = -3.333333333

The k term is -7k.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7k + 12.25 + k2 = -3.333333333 + 12.25

Reorder the terms:
12.25 + -7k + k2 = -3.333333333 + 12.25

Combine like terms: -3.333333333 + 12.25 = 8.916666667
12.25 + -7k + k2 = 8.916666667

Factor a perfect square on the left side:
(k + -3.5)(k + -3.5) = 8.916666667

Calculate the square root of the right side: 2.986078811

Break this problem into two subproblems by setting 
(k + -3.5) equal to 2.986078811 and -2.986078811.

Subproblem 1

k + -3.5 = 2.986078811 Simplifying k + -3.5 = 2.986078811 Reorder the terms: -3.5 + k = 2.986078811 Solving -3.5 + k = 2.986078811 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = 2.986078811 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = 2.986078811 + 3.5 k = 2.986078811 + 3.5 Combine like terms: 2.986078811 + 3.5 = 6.486078811 k = 6.486078811 Simplifying k = 6.486078811

Subproblem 2

k + -3.5 = -2.986078811 Simplifying k + -3.5 = -2.986078811 Reorder the terms: -3.5 + k = -2.986078811 Solving -3.5 + k = -2.986078811 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = -2.986078811 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = -2.986078811 + 3.5 k = -2.986078811 + 3.5 Combine like terms: -2.986078811 + 3.5 = 0.513921189 k = 0.513921189 Simplifying k = 0.513921189

Solution

The solution to the problem is based on the solutions from the subproblems. k = {6.486078811, 0.513921189}

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