(5k-1)(5k-1)=-27

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Solution for (5k-1)(5k-1)=-27 equation: 


Simplifying
(5k + -1)(5k + -1) = -27

Reorder the terms:
(-1 + 5k)(5k + -1) = -27

Reorder the terms:
(-1 + 5k)(-1 + 5k) = -27

Multiply (-1 + 5k) * (-1 + 5k)
(-1(-1 + 5k) + 5k * (-1 + 5k)) = -27
((-1 * -1 + 5k * -1) + 5k * (-1 + 5k)) = -27
((1 + -5k) + 5k * (-1 + 5k)) = -27
(1 + -5k + (-1 * 5k + 5k * 5k)) = -27
(1 + -5k + (-5k + 25k2)) = -27

Combine like terms: -5k + -5k = -10k
(1 + -10k + 25k2) = -27

Solving
1 + -10k + 25k2 = -27

Solving for variable 'k'.

Reorder the terms:
1 + 27 + -10k + 25k2 = -27 + 27

Combine like terms: 1 + 27 = 28
28 + -10k + 25k2 = -27 + 27

Combine like terms: -27 + 27 = 0
28 + -10k + 25k2 = 0

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

Divide each side by '25'.
1.12 + -0.4k + k2 = 0

Move the constant term to the right:

Add '-1.12' to each side of the equation.
1.12 + -0.4k + -1.12 + k2 = 0 + -1.12

Reorder the terms:
1.12 + -1.12 + -0.4k + k2 = 0 + -1.12

Combine like terms: 1.12 + -1.12 = 0.00
0.00 + -0.4k + k2 = 0 + -1.12
-0.4k + k2 = 0 + -1.12

Combine like terms: 0 + -1.12 = -1.12
-0.4k + k2 = -1.12

The k term is -0.4k.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4k + 0.04 + k2 = -1.12 + 0.04

Reorder the terms:
0.04 + -0.4k + k2 = -1.12 + 0.04

Combine like terms: -1.12 + 0.04 = -1.08
0.04 + -0.4k + k2 = -1.08

Factor a perfect square on the left side:
(k + -0.2)(k + -0.2) = -1.08

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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