-k(k+1)=9

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Solution for -k(k+1)=9 equation: 


Simplifying
-1k(k + 1) = 9

Reorder the terms:
-1k(1 + k) = 9
(1 * -1k + k * -1k) = 9
(-1k + -1k2) = 9

Solving
-1k + -1k2 = 9

Solving for variable 'k'.

Reorder the terms:
-9 + -1k + -1k2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -1k + -1k2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + k + k2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + k + k2)' equal to zero and attempt to solve:

Simplifying
9 + k + k2 = 0

Solving
9 + k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + k + -9 + k2 = 0 + -9

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

Combine like terms: 9 + -9 = 0
0 + k + k2 = 0 + -9
k + k2 = 0 + -9

Combine like terms: 0 + -9 = -9
k + k2 = -9

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
k + 0.25 + k2 = -9 + 0.25

Reorder the terms:
0.25 + k + k2 = -9 + 0.25

Combine like terms: -9 + 0.25 = -8.75
0.25 + k + k2 = -8.75

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = -8.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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