8+s(s-1)=18

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Solution for 8+s(s-1)=18 equation:


Simplifying
8 + s(s + -1) = 18

Reorder the terms:
8 + s(-1 + s) = 18
8 + (-1 * s + s * s) = 18
8 + (-1s + s2) = 18

Solving
8 + -1s + s2 = 18

Solving for variable 's'.

Reorder the terms:
8 + -18 + -1s + s2 = 18 + -18

Combine like terms: 8 + -18 = -10
-10 + -1s + s2 = 18 + -18

Combine like terms: 18 + -18 = 0
-10 + -1s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -1s + 10 + s2 = 0 + 10

Reorder the terms:
-10 + 10 + -1s + s2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1s + s2 = 0 + 10
-1s + s2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1s + s2 = 10

The s term is -1s.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1s + 0.25 + s2 = 10 + 0.25

Reorder the terms:
0.25 + -1s + s2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
0.25 + -1s + s2 = 10.25

Factor a perfect square on the left side:
(s + -0.5)(s + -0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(s + -0.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

s + -0.5 = 3.201562119 Simplifying s + -0.5 = 3.201562119 Reorder the terms: -0.5 + s = 3.201562119 Solving -0.5 + s = 3.201562119 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = 3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = 3.201562119 + 0.5 s = 3.201562119 + 0.5 Combine like terms: 3.201562119 + 0.5 = 3.701562119 s = 3.701562119 Simplifying s = 3.701562119

Subproblem 2

s + -0.5 = -3.201562119 Simplifying s + -0.5 = -3.201562119 Reorder the terms: -0.5 + s = -3.201562119 Solving -0.5 + s = -3.201562119 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + s = -3.201562119 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + s = -3.201562119 + 0.5 s = -3.201562119 + 0.5 Combine like terms: -3.201562119 + 0.5 = -2.701562119 s = -2.701562119 Simplifying s = -2.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. s = {3.701562119, -2.701562119}

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