k^2-28k-1=0

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Solution for k^2-28k-1=0 equation:


Simplifying
k2 + -28k + -1 = 0

Reorder the terms:
-1 + -28k + k2 = 0

Solving
-1 + -28k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -28k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + -28k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -28k + k2 = 0 + 1
-28k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
-28k + k2 = 1

The k term is -28k.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28k + 196 + k2 = 1 + 196

Reorder the terms:
196 + -28k + k2 = 1 + 196

Combine like terms: 1 + 196 = 197
196 + -28k + k2 = 197

Factor a perfect square on the left side:
(k + -14)(k + -14) = 197

Calculate the square root of the right side: 14.035668848

Break this problem into two subproblems by setting 
(k + -14) equal to 14.035668848 and -14.035668848.

Subproblem 1

k + -14 = 14.035668848 Simplifying k + -14 = 14.035668848 Reorder the terms: -14 + k = 14.035668848 Solving -14 + k = 14.035668848 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = 14.035668848 + 14 Combine like terms: -14 + 14 = 0 0 + k = 14.035668848 + 14 k = 14.035668848 + 14 Combine like terms: 14.035668848 + 14 = 28.035668848 k = 28.035668848 Simplifying k = 28.035668848

Subproblem 2

k + -14 = -14.035668848 Simplifying k + -14 = -14.035668848 Reorder the terms: -14 + k = -14.035668848 Solving -14 + k = -14.035668848 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + k = -14.035668848 + 14 Combine like terms: -14 + 14 = 0 0 + k = -14.035668848 + 14 k = -14.035668848 + 14 Combine like terms: -14.035668848 + 14 = -0.035668848 k = -0.035668848 Simplifying k = -0.035668848

Solution

The solution to the problem is based on the solutions from the subproblems. k = {28.035668848, -0.035668848}

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