(9k-1)(9k-1)=-125

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Solution for (9k-1)(9k-1)=-125 equation: 


Simplifying
(9k + -1)(9k + -1) = -125

Reorder the terms:
(-1 + 9k)(9k + -1) = -125

Reorder the terms:
(-1 + 9k)(-1 + 9k) = -125

Multiply (-1 + 9k) * (-1 + 9k)
(-1(-1 + 9k) + 9k * (-1 + 9k)) = -125
((-1 * -1 + 9k * -1) + 9k * (-1 + 9k)) = -125
((1 + -9k) + 9k * (-1 + 9k)) = -125
(1 + -9k + (-1 * 9k + 9k * 9k)) = -125
(1 + -9k + (-9k + 81k2)) = -125

Combine like terms: -9k + -9k = -18k
(1 + -18k + 81k2) = -125

Solving
1 + -18k + 81k2 = -125

Solving for variable 'k'.

Reorder the terms:
1 + 125 + -18k + 81k2 = -125 + 125

Combine like terms: 1 + 125 = 126
126 + -18k + 81k2 = -125 + 125

Combine like terms: -125 + 125 = 0
126 + -18k + 81k2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(14 + -2k + 9k2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(14 + -2k + 9k2)' equal to zero and attempt to solve:

Simplifying
14 + -2k + 9k2 = 0

Solving
14 + -2k + 9k2 = 0

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

Divide each side by '9'.
1.555555556 + -0.2222222222k + k2 = 0

Move the constant term to the right:

Add '-1.555555556' to each side of the equation.
1.555555556 + -0.2222222222k + -1.555555556 + k2 = 0 + -1.555555556

Reorder the terms:
1.555555556 + -1.555555556 + -0.2222222222k + k2 = 0 + -1.555555556

Combine like terms: 1.555555556 + -1.555555556 = 0.000000000
0.000000000 + -0.2222222222k + k2 = 0 + -1.555555556
-0.2222222222k + k2 = 0 + -1.555555556

Combine like terms: 0 + -1.555555556 = -1.555555556
-0.2222222222k + k2 = -1.555555556

The k term is -0.2222222222k.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222k + 0.01234567901 + k2 = -1.555555556 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222k + k2 = -1.555555556 + 0.01234567901

Combine like terms: -1.555555556 + 0.01234567901 = -1.54320987699
0.01234567901 + -0.2222222222k + k2 = -1.54320987699

Factor a perfect square on the left side:
(k + -0.1111111111)(k + -0.1111111111) = -1.54320987699

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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