39.671192x^2-x=443.432625675216

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Solution for 39.671192x^2-x=443.432625675216 equation:


Simplifying
39.671192x2 + -1x = 443.432625675216

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

Solving
-1x + 39.671192x2 = 443.432625675216

Solving for variable 'x'.

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

Combine like terms: 443.432625675216 + -443.432625675216 = 0.000000000000
-443.432625675216 + -1x + 39.671192x2 = 0.000000000000

Begin completing the square.  Divide all terms by
39.671192 the coefficient of the squared term: 

Divide each side by '39.671192'.
-11.17769856 + -0.02520720829x + x2 = 0.000000

Move the constant term to the right:

Add '11.17769856' to each side of the equation.
-11.17769856 + -0.02520720829x + 11.17769856 + x2 = 0.000000 + 11.17769856

Reorder the terms:
-11.17769856 + 11.17769856 + -0.02520720829x + x2 = 0.000000 + 11.17769856

Combine like terms: -11.17769856 + 11.17769856 = 0.00000000
0.00000000 + -0.02520720829x + x2 = 0.000000 + 11.17769856
-0.02520720829x + x2 = 0.000000 + 11.17769856

Combine like terms: 0.000000 + 11.17769856 = 11.17769856
-0.02520720829x + x2 = 11.17769856

The x term is -0.02520720829x.  Take half its coefficient (-0.01260360415).
Square it (0.0001588508376) and add it to both sides.

Add '0.0001588508376' to each side of the equation.
-0.02520720829x + 0.0001588508376 + x2 = 11.17769856 + 0.0001588508376

Reorder the terms:
0.0001588508376 + -0.02520720829x + x2 = 11.17769856 + 0.0001588508376

Combine like terms: 11.17769856 + 0.0001588508376 = 11.1778574108376
0.0001588508376 + -0.02520720829x + x2 = 11.1778574108376

Factor a perfect square on the left side:
(x + -0.01260360415)(x + -0.01260360415) = 11.1778574108376

Calculate the square root of the right side: 3.343330287

Break this problem into two subproblems by setting 
(x + -0.01260360415) equal to 3.343330287 and -3.343330287.

Subproblem 1

x + -0.01260360415 = 3.343330287 Simplifying x + -0.01260360415 = 3.343330287 Reorder the terms: -0.01260360415 + x = 3.343330287 Solving -0.01260360415 + x = 3.343330287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01260360415' to each side of the equation. -0.01260360415 + 0.01260360415 + x = 3.343330287 + 0.01260360415 Combine like terms: -0.01260360415 + 0.01260360415 = 0.00000000000 0.00000000000 + x = 3.343330287 + 0.01260360415 x = 3.343330287 + 0.01260360415 Combine like terms: 3.343330287 + 0.01260360415 = 3.35593389115 x = 3.35593389115 Simplifying x = 3.35593389115

Subproblem 2

x + -0.01260360415 = -3.343330287 Simplifying x + -0.01260360415 = -3.343330287 Reorder the terms: -0.01260360415 + x = -3.343330287 Solving -0.01260360415 + x = -3.343330287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01260360415' to each side of the equation. -0.01260360415 + 0.01260360415 + x = -3.343330287 + 0.01260360415 Combine like terms: -0.01260360415 + 0.01260360415 = 0.00000000000 0.00000000000 + x = -3.343330287 + 0.01260360415 x = -3.343330287 + 0.01260360415 Combine like terms: -3.343330287 + 0.01260360415 = -3.33072668285 x = -3.33072668285 Simplifying x = -3.33072668285

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.35593389115, -3.33072668285}

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