k(3k+1)+(k+1)=

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Solution for k(3k+1)+(k+1)= equation: 


Simplifying
k(3k + 1) + (k + 1) = 0

Reorder the terms:
k(1 + 3k) + (k + 1) = 0
(1 * k + 3k * k) + (k + 1) = 0
(1k + 3k2) + (k + 1) = 0

Reorder the terms:
1k + 3k2 + (1 + k) = 0

Remove parenthesis around (1 + k)
1k + 3k2 + 1 + k = 0

Reorder the terms:
1 + 1k + k + 3k2 = 0

Combine like terms: 1k + k = 2k
1 + 2k + 3k2 = 0

Solving
1 + 2k + 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'.
0.3333333333 + 0.6666666667k + k2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 0.6666666667k + -0.3333333333 + k2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 0.6666666667k + k2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 0.6666666667k + k2 = 0 + -0.3333333333
0.6666666667k + k2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.6666666667k + k2 = -0.3333333333

The k term is 0.6666666667k.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667k + 0.1111111112 + k2 = -0.3333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667k + k2 = -0.3333333333 + 0.1111111112

Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221
0.1111111112 + 0.6666666667k + k2 = -0.2222222221

Factor a perfect square on the left side:
(k + 0.3333333334)(k + 0.3333333334) = -0.2222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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