s^2-2s-10=0

Solution for s^2-2s-10=0 equation:

Simplifying
s2 + -2s + -10 = 0

Reorder the terms:
-10 + -2s + s2 = 0

Solving
-10 + -2s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2s + 10 + s2 = 0 + 10

Reorder the terms:
-10 + 10 + -2s + s2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2s + s2 = 0 + 10
-2s + s2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2s + s2 = 10

The s term is -2s.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2s + 1 + s2 = 10 + 1

Reorder the terms:
1 + -2s + s2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2s + s2 = 11

Factor a perfect square on the left side:
(s + -1)(s + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(s + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1
s + -1 = 3.31662479

Simplifying
s + -1 = 3.31662479

Reorder the terms:
-1 + s = 3.31662479

Solving
-1 + s = 3.31662479

Solving for variable 's'.

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

Add '1' to each side of the equation.
-1 + 1 + s = 3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + s = 3.31662479 + 1
s = 3.31662479 + 1

Combine like terms: 3.31662479 + 1 = 4.31662479
s = 4.31662479

Simplifying
s = 4.31662479

Subproblem 2
s + -1 = -3.31662479

Simplifying
s + -1 = -3.31662479

Reorder the terms:
-1 + s = -3.31662479

Solving
-1 + s = -3.31662479

Solving for variable 's'.

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

Add '1' to each side of the equation.
-1 + 1 + s = -3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + s = -3.31662479 + 1
s = -3.31662479 + 1

Combine like terms: -3.31662479 + 1 = -2.31662479
s = -2.31662479

Simplifying
s = -2.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {4.31662479, -2.31662479}