k^2-4k+1=0

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Solution for k^2-4k+1=0 equation:


Simplifying
k2 + -4k + 1 = 0

Reorder the terms:
1 + -4k + k2 = 0

Solving
1 + -4k + 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 + -4k + -1 + k2 = 0 + -1

Reorder the terms:
1 + -1 + -4k + k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4k + k2 = 0 + -1
-4k + k2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4k + k2 = -1

The k term is -4k.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k + 4 + k2 = -1 + 4

Reorder the terms:
4 + -4k + k2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + -4k + k2 = 3

Factor a perfect square on the left side:
(k + -2)(k + -2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(k + -2) equal to 1.732050808 and -1.732050808.

Subproblem 1

k + -2 = 1.732050808 Simplifying k + -2 = 1.732050808 Reorder the terms: -2 + k = 1.732050808 Solving -2 + k = 1.732050808 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + k = 1.732050808 + 2 k = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 k = 3.732050808 Simplifying k = 3.732050808

Subproblem 2

k + -2 = -1.732050808 Simplifying k + -2 = -1.732050808 Reorder the terms: -2 + k = -1.732050808 Solving -2 + k = -1.732050808 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + k = -1.732050808 + 2 k = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 k = 0.267949192 Simplifying k = 0.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. k = {3.732050808, 0.267949192}

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