-1x^2-39.671192x+443.432625675216=0

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Solution for -1x^2-39.671192x+443.432625675216=0 equation:


Simplifying
-1x2 + -39.671192x + 443.432625675216 = 0

Reorder the terms:
443.432625675216 + -39.671192x + -1x2 = 0

Solving
443.432625675216 + -39.671192x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-443.4326257 + 39.671192x + x2 = 0

Move the constant term to the right:

Add '443.4326257' to each side of the equation.
-443.4326257 + 39.671192x + 443.4326257 + x2 = 0 + 443.4326257

Reorder the terms:
-443.4326257 + 443.4326257 + 39.671192x + x2 = 0 + 443.4326257

Combine like terms: -443.4326257 + 443.4326257 = 0.0000000
0.0000000 + 39.671192x + x2 = 0 + 443.4326257
39.671192x + x2 = 0 + 443.4326257

Combine like terms: 0 + 443.4326257 = 443.4326257
39.671192x + x2 = 443.4326257

The x term is 39.671192x.  Take half its coefficient (19.835596).
Square it (393.4508687) and add it to both sides.

Add '393.4508687' to each side of the equation.
39.671192x + 393.4508687 + x2 = 443.4326257 + 393.4508687

Reorder the terms:
393.4508687 + 39.671192x + x2 = 443.4326257 + 393.4508687

Combine like terms: 443.4326257 + 393.4508687 = 836.8834944
393.4508687 + 39.671192x + x2 = 836.8834944

Factor a perfect square on the left side:
(x + 19.835596)(x + 19.835596) = 836.8834944

Calculate the square root of the right side: 28.928938702

Break this problem into two subproblems by setting 
(x + 19.835596) equal to 28.928938702 and -28.928938702.

Subproblem 1

x + 19.835596 = 28.928938702 Simplifying x + 19.835596 = 28.928938702 Reorder the terms: 19.835596 + x = 28.928938702 Solving 19.835596 + x = 28.928938702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.835596' to each side of the equation. 19.835596 + -19.835596 + x = 28.928938702 + -19.835596 Combine like terms: 19.835596 + -19.835596 = 0.000000 0.000000 + x = 28.928938702 + -19.835596 x = 28.928938702 + -19.835596 Combine like terms: 28.928938702 + -19.835596 = 9.093342702 x = 9.093342702 Simplifying x = 9.093342702

Subproblem 2

x + 19.835596 = -28.928938702 Simplifying x + 19.835596 = -28.928938702 Reorder the terms: 19.835596 + x = -28.928938702 Solving 19.835596 + x = -28.928938702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19.835596' to each side of the equation. 19.835596 + -19.835596 + x = -28.928938702 + -19.835596 Combine like terms: 19.835596 + -19.835596 = 0.000000 0.000000 + x = -28.928938702 + -19.835596 x = -28.928938702 + -19.835596 Combine like terms: -28.928938702 + -19.835596 = -48.764534702 x = -48.764534702 Simplifying x = -48.764534702

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.093342702, -48.764534702}

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