10+k=9k+4-3k^2

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Solution for 10+k=9k+4-3k^2 equation: 


Simplifying
10 + k = 9k + 4 + -3k2

Reorder the terms:
10 + k = 4 + 9k + -3k2

Solving
10 + k = 4 + 9k + -3k2

Solving for variable 'k'.

Reorder the terms:
10 + -4 + k + -9k + 3k2 = 4 + 9k + -3k2 + -4 + -9k + 3k2

Combine like terms: 10 + -4 = 6
6 + k + -9k + 3k2 = 4 + 9k + -3k2 + -4 + -9k + 3k2

Combine like terms: k + -9k = -8k
6 + -8k + 3k2 = 4 + 9k + -3k2 + -4 + -9k + 3k2

Reorder the terms:
6 + -8k + 3k2 = 4 + -4 + 9k + -9k + -3k2 + 3k2

Combine like terms: 4 + -4 = 0
6 + -8k + 3k2 = 0 + 9k + -9k + -3k2 + 3k2
6 + -8k + 3k2 = 9k + -9k + -3k2 + 3k2

Combine like terms: 9k + -9k = 0
6 + -8k + 3k2 = 0 + -3k2 + 3k2
6 + -8k + 3k2 = -3k2 + 3k2

Combine like terms: -3k2 + 3k2 = 0
6 + -8k + 3k2 = 0

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

Divide each side by '3'.
2 + -2.666666667k + k2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2.666666667k + -2 + k2 = 0 + -2

Reorder the terms:
2 + -2 + -2.666666667k + k2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2.666666667k + k2 = 0 + -2
-2.666666667k + k2 = 0 + -2

Combine like terms: 0 + -2 = -2
-2.666666667k + k2 = -2

The k term is -2.666666667k.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667k + 1.777777780 + k2 = -2 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667k + k2 = -2 + 1.777777780

Combine like terms: -2 + 1.777777780 = -0.22222222
1.777777780 + -2.666666667k + k2 = -0.22222222

Factor a perfect square on the left side:
(k + -1.333333334)(k + -1.333333334) = -0.22222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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