41x^2+100x-3600=0

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Solution for 41x^2+100x-3600=0 equation:


Simplifying
41x2 + 100x + -3600 = 0

Reorder the terms:
-3600 + 100x + 41x2 = 0

Solving
-3600 + 100x + 41x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
41 the coefficient of the squared term: 

Divide each side by '41'.
-87.80487805 + 2.43902439x + x2 = 0

Move the constant term to the right:

Add '87.80487805' to each side of the equation.
-87.80487805 + 2.43902439x + 87.80487805 + x2 = 0 + 87.80487805

Reorder the terms:
-87.80487805 + 87.80487805 + 2.43902439x + x2 = 0 + 87.80487805

Combine like terms: -87.80487805 + 87.80487805 = 0.00000000
0.00000000 + 2.43902439x + x2 = 0 + 87.80487805
2.43902439x + x2 = 0 + 87.80487805

Combine like terms: 0 + 87.80487805 = 87.80487805
2.43902439x + x2 = 87.80487805

The x term is 2.43902439x.  Take half its coefficient (1.219512195).
Square it (1.487209994) and add it to both sides.

Add '1.487209994' to each side of the equation.
2.43902439x + 1.487209994 + x2 = 87.80487805 + 1.487209994

Reorder the terms:
1.487209994 + 2.43902439x + x2 = 87.80487805 + 1.487209994

Combine like terms: 87.80487805 + 1.487209994 = 89.292088044
1.487209994 + 2.43902439x + x2 = 89.292088044

Factor a perfect square on the left side:
(x + 1.219512195)(x + 1.219512195) = 89.292088044

Calculate the square root of the right side: 9.449449087

Break this problem into two subproblems by setting 
(x + 1.219512195) equal to 9.449449087 and -9.449449087.

Subproblem 1

x + 1.219512195 = 9.449449087 Simplifying x + 1.219512195 = 9.449449087 Reorder the terms: 1.219512195 + x = 9.449449087 Solving 1.219512195 + x = 9.449449087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.219512195' to each side of the equation. 1.219512195 + -1.219512195 + x = 9.449449087 + -1.219512195 Combine like terms: 1.219512195 + -1.219512195 = 0.000000000 0.000000000 + x = 9.449449087 + -1.219512195 x = 9.449449087 + -1.219512195 Combine like terms: 9.449449087 + -1.219512195 = 8.229936892 x = 8.229936892 Simplifying x = 8.229936892

Subproblem 2

x + 1.219512195 = -9.449449087 Simplifying x + 1.219512195 = -9.449449087 Reorder the terms: 1.219512195 + x = -9.449449087 Solving 1.219512195 + x = -9.449449087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.219512195' to each side of the equation. 1.219512195 + -1.219512195 + x = -9.449449087 + -1.219512195 Combine like terms: 1.219512195 + -1.219512195 = 0.000000000 0.000000000 + x = -9.449449087 + -1.219512195 x = -9.449449087 + -1.219512195 Combine like terms: -9.449449087 + -1.219512195 = -10.668961282 x = -10.668961282 Simplifying x = -10.668961282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.229936892, -10.668961282}

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