s^2+82s-1948566=0

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Solution for s^2+82s-1948566=0 equation:


Simplifying
s2 + 82s + -1948566 = 0

Reorder the terms:
-1948566 + 82s + s2 = 0

Solving
-1948566 + 82s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '1948566' to each side of the equation.
-1948566 + 82s + 1948566 + s2 = 0 + 1948566

Reorder the terms:
-1948566 + 1948566 + 82s + s2 = 0 + 1948566

Combine like terms: -1948566 + 1948566 = 0
0 + 82s + s2 = 0 + 1948566
82s + s2 = 0 + 1948566

Combine like terms: 0 + 1948566 = 1948566
82s + s2 = 1948566

The s term is 82s.  Take half its coefficient (41).
Square it (1681) and add it to both sides.

Add '1681' to each side of the equation.
82s + 1681 + s2 = 1948566 + 1681

Reorder the terms:
1681 + 82s + s2 = 1948566 + 1681

Combine like terms: 1948566 + 1681 = 1950247
1681 + 82s + s2 = 1950247

Factor a perfect square on the left side:
(s + 41)(s + 41) = 1950247

Calculate the square root of the right side: 1396.512441763

Break this problem into two subproblems by setting 
(s + 41) equal to 1396.512441763 and -1396.512441763.

Subproblem 1

s + 41 = 1396.512441763 Simplifying s + 41 = 1396.512441763 Reorder the terms: 41 + s = 1396.512441763 Solving 41 + s = 1396.512441763 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + s = 1396.512441763 + -41 Combine like terms: 41 + -41 = 0 0 + s = 1396.512441763 + -41 s = 1396.512441763 + -41 Combine like terms: 1396.512441763 + -41 = 1355.512441763 s = 1355.512441763 Simplifying s = 1355.512441763

Subproblem 2

s + 41 = -1396.512441763 Simplifying s + 41 = -1396.512441763 Reorder the terms: 41 + s = -1396.512441763 Solving 41 + s = -1396.512441763 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-41' to each side of the equation. 41 + -41 + s = -1396.512441763 + -41 Combine like terms: 41 + -41 = 0 0 + s = -1396.512441763 + -41 s = -1396.512441763 + -41 Combine like terms: -1396.512441763 + -41 = -1437.512441763 s = -1437.512441763 Simplifying s = -1437.512441763

Solution

The solution to the problem is based on the solutions from the subproblems. s = {1355.512441763, -1437.512441763}

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