s^2-3s=1

Solution for s^2-3s=1 equation:

Simplifying
s2 + -3s = 1

Reorder the terms:
-3s + s2 = 1

Solving
-3s + s2 = 1

Solving for variable 's'.

Reorder the terms:
-1 + -3s + s2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -3s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3s + 1 + s2 = 0 + 1

Reorder the terms:
-1 + 1 + -3s + s2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3s + s2 = 0 + 1
-3s + s2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3s + s2 = 1

The s term is -3s.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3s + 2.25 + s2 = 1 + 2.25

Reorder the terms:
2.25 + -3s + s2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3s + s2 = 3.25

Factor a perfect square on the left side:
(s + -1.5)(s + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(s + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
s + -1.5 = 1.802775638

Simplifying
s + -1.5 = 1.802775638

Reorder the terms:
-1.5 + s = 1.802775638

Solving
-1.5 + s = 1.802775638

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = 1.802775638 + 1.5
s = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
s = 3.302775638

Simplifying
s = 3.302775638

Subproblem 2
s + -1.5 = -1.802775638

Simplifying
s + -1.5 = -1.802775638

Reorder the terms:
-1.5 + s = -1.802775638

Solving
-1.5 + s = -1.802775638

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = -1.802775638 + 1.5
s = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
s = -0.302775638

Simplifying
s = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {3.302775638, -0.302775638}