9k^2-84k+4=0

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Solution for 9k^2-84k+4=0 equation:


Simplifying
9k2 + -84k + 4 = 0

Reorder the terms:
4 + -84k + 9k2 = 0

Solving
4 + -84k + 9k2 = 0

Solving for variable 'k'.

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

Divide each side by '9'.
0.4444444444 + -9.333333333k + k2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -9.333333333k + -0.4444444444 + k2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -9.333333333k + k2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -9.333333333k + k2 = 0 + -0.4444444444
-9.333333333k + k2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-9.333333333k + k2 = -0.4444444444

The k term is -9.333333333k.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333k + 21.77777778 + k2 = -0.4444444444 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333k + k2 = -0.4444444444 + 21.77777778

Combine like terms: -0.4444444444 + 21.77777778 = 21.3333333356
21.77777778 + -9.333333333k + k2 = 21.3333333356

Factor a perfect square on the left side:
(k + -4.666666667)(k + -4.666666667) = 21.3333333356

Calculate the square root of the right side: 4.618802154

Break this problem into two subproblems by setting 
(k + -4.666666667) equal to 4.618802154 and -4.618802154.

Subproblem 1

k + -4.666666667 = 4.618802154 Simplifying k + -4.666666667 = 4.618802154 Reorder the terms: -4.666666667 + k = 4.618802154 Solving -4.666666667 + k = 4.618802154 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + k = 4.618802154 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + k = 4.618802154 + 4.666666667 k = 4.618802154 + 4.666666667 Combine like terms: 4.618802154 + 4.666666667 = 9.285468821 k = 9.285468821 Simplifying k = 9.285468821

Subproblem 2

k + -4.666666667 = -4.618802154 Simplifying k + -4.666666667 = -4.618802154 Reorder the terms: -4.666666667 + k = -4.618802154 Solving -4.666666667 + k = -4.618802154 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + k = -4.618802154 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + k = -4.618802154 + 4.666666667 k = -4.618802154 + 4.666666667 Combine like terms: -4.618802154 + 4.666666667 = 0.047864513 k = 0.047864513 Simplifying k = 0.047864513

Solution

The solution to the problem is based on the solutions from the subproblems. k = {9.285468821, 0.047864513}

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