s^2-6s+1=0

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Solution for s^2-6s+1=0 equation:


Simplifying
s2 + -6s + 1 = 0

Reorder the terms:
1 + -6s + s2 = 0

Solving
1 + -6s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -6s + -1 + s2 = 0 + -1

Reorder the terms:
1 + -1 + -6s + s2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6s + s2 = 0 + -1
-6s + s2 = 0 + -1

Combine like terms: 0 + -1 = -1
-6s + s2 = -1

The s term is -6s.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6s + 9 + s2 = -1 + 9

Reorder the terms:
9 + -6s + s2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + -6s + s2 = 8

Factor a perfect square on the left side:
(s + -3)(s + -3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(s + -3) equal to 2.828427125 and -2.828427125.

Subproblem 1

s + -3 = 2.828427125 Simplifying s + -3 = 2.828427125 Reorder the terms: -3 + s = 2.828427125 Solving -3 + s = 2.828427125 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + s = 2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + s = 2.828427125 + 3 s = 2.828427125 + 3 Combine like terms: 2.828427125 + 3 = 5.828427125 s = 5.828427125 Simplifying s = 5.828427125

Subproblem 2

s + -3 = -2.828427125 Simplifying s + -3 = -2.828427125 Reorder the terms: -3 + s = -2.828427125 Solving -3 + s = -2.828427125 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + s = -2.828427125 + 3 Combine like terms: -3 + 3 = 0 0 + s = -2.828427125 + 3 s = -2.828427125 + 3 Combine like terms: -2.828427125 + 3 = 0.171572875 s = 0.171572875 Simplifying s = 0.171572875

Solution

The solution to the problem is based on the solutions from the subproblems. s = {5.828427125, 0.171572875}

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