(s+1+2)*(s)=30

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Solution for (s+1+2)*(s)=30 equation:


Simplifying
(s + 1 + 2)(s) = 30

Reorder the terms:
(1 + 2 + s)(s) = 30

Combine like terms: 1 + 2 = 3
(3 + s)(s) = 30

Reorder the terms for easier multiplication:
s(3 + s) = 30
(3 * s + s * s) = 30
(3s + s2) = 30

Solving
3s + s2 = 30

Solving for variable 's'.

Reorder the terms:
-30 + 3s + s2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 3s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 3s + 30 + s2 = 0 + 30

Reorder the terms:
-30 + 30 + 3s + s2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 3s + s2 = 0 + 30
3s + s2 = 0 + 30

Combine like terms: 0 + 30 = 30
3s + s2 = 30

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 = 30 + 2.25

Reorder the terms:
2.25 + 3s + s2 = 30 + 2.25

Combine like terms: 30 + 2.25 = 32.25
2.25 + 3s + s2 = 32.25

Factor a perfect square on the left side:
(s + 1.5)(s + 1.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(s + 1.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

s + 1.5 = 5.678908346 Simplifying s + 1.5 = 5.678908346 Reorder the terms: 1.5 + s = 5.678908346 Solving 1.5 + s = 5.678908346 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 = 5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = 5.678908346 + -1.5 s = 5.678908346 + -1.5 Combine like terms: 5.678908346 + -1.5 = 4.178908346 s = 4.178908346 Simplifying s = 4.178908346

Subproblem 2

s + 1.5 = -5.678908346 Simplifying s + 1.5 = -5.678908346 Reorder the terms: 1.5 + s = -5.678908346 Solving 1.5 + s = -5.678908346 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 = -5.678908346 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = -5.678908346 + -1.5 s = -5.678908346 + -1.5 Combine like terms: -5.678908346 + -1.5 = -7.178908346 s = -7.178908346 Simplifying s = -7.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. s = {4.178908346, -7.178908346}

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