s^2-5=4s+36

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Solution for s^2-5=4s+36 equation:


Simplifying
s2 + -5 = 4s + 36

Reorder the terms:
-5 + s2 = 4s + 36

Reorder the terms:
-5 + s2 = 36 + 4s

Solving
-5 + s2 = 36 + 4s

Solving for variable 's'.

Reorder the terms:
-5 + -36 + -4s + s2 = 36 + 4s + -36 + -4s

Combine like terms: -5 + -36 = -41
-41 + -4s + s2 = 36 + 4s + -36 + -4s

Reorder the terms:
-41 + -4s + s2 = 36 + -36 + 4s + -4s

Combine like terms: 36 + -36 = 0
-41 + -4s + s2 = 0 + 4s + -4s
-41 + -4s + s2 = 4s + -4s

Combine like terms: 4s + -4s = 0
-41 + -4s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + -4s + 41 + s2 = 0 + 41

Reorder the terms:
-41 + 41 + -4s + s2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -4s + s2 = 0 + 41
-4s + s2 = 0 + 41

Combine like terms: 0 + 41 = 41
-4s + s2 = 41

The s term is -4s.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4s + 4 + s2 = 41 + 4

Reorder the terms:
4 + -4s + s2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + -4s + s2 = 45

Factor a perfect square on the left side:
(s + -2)(s + -2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(s + -2) equal to 6.708203933 and -6.708203933.

Subproblem 1

s + -2 = 6.708203933 Simplifying s + -2 = 6.708203933 Reorder the terms: -2 + s = 6.708203933 Solving -2 + s = 6.708203933 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = 6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + s = 6.708203933 + 2 s = 6.708203933 + 2 Combine like terms: 6.708203933 + 2 = 8.708203933 s = 8.708203933 Simplifying s = 8.708203933

Subproblem 2

s + -2 = -6.708203933 Simplifying s + -2 = -6.708203933 Reorder the terms: -2 + s = -6.708203933 Solving -2 + s = -6.708203933 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + s = -6.708203933 + 2 Combine like terms: -2 + 2 = 0 0 + s = -6.708203933 + 2 s = -6.708203933 + 2 Combine like terms: -6.708203933 + 2 = -4.708203933 s = -4.708203933 Simplifying s = -4.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. s = {8.708203933, -4.708203933}

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