s(s-3)=38

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Solution for s(s-3)=38 equation: 


Simplifying
s(s + -3) = 38

Reorder the terms:
s(-3 + s) = 38
(-3 * s + s * s) = 38
(-3s + s2) = 38

Solving
-3s + s2 = 38

Solving for variable 's'.

Reorder the terms:
-38 + -3s + s2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + -3s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -3s + 38 + s2 = 0 + 38

Reorder the terms:
-38 + 38 + -3s + s2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -3s + s2 = 0 + 38
-3s + s2 = 0 + 38

Combine like terms: 0 + 38 = 38
-3s + s2 = 38

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 = 38 + 2.25

Reorder the terms:
2.25 + -3s + s2 = 38 + 2.25

Combine like terms: 38 + 2.25 = 40.25
2.25 + -3s + s2 = 40.25

Factor a perfect square on the left side:
(s + -1.5)(s + -1.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(s + -1.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
s + -1.5 = 6.34428877

Simplifying
s + -1.5 = 6.34428877

Reorder the terms:
-1.5 + s = 6.34428877

Solving
-1.5 + s = 6.34428877

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 = 6.34428877 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = 6.34428877 + 1.5
s = 6.34428877 + 1.5

Combine like terms: 6.34428877 + 1.5 = 7.84428877
s = 7.84428877

Simplifying
s = 7.84428877


Subproblem 2
s + -1.5 = -6.34428877

Simplifying
s + -1.5 = -6.34428877

Reorder the terms:
-1.5 + s = -6.34428877

Solving
-1.5 + s = -6.34428877

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 = -6.34428877 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = -6.34428877 + 1.5
s = -6.34428877 + 1.5

Combine like terms: -6.34428877 + 1.5 = -4.84428877
s = -4.84428877

Simplifying
s = -4.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {7.84428877, -4.84428877}

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