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Simplifying -39.671192x2 + -1x + 443.432625675216 = 0 Reorder the terms: 443.432625675216 + -1x + -39.671192x2 = 0 Solving 443.432625675216 + -1x + -39.671192x2 = 0 Solving for variable 'x'. 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 Move the constant term to the right: Add '11.17769856' to each side of the equation. -11.17769856 + 0.02520720829x + 11.17769856 + x2 = 0 + 11.17769856 Reorder the terms: -11.17769856 + 11.17769856 + 0.02520720829x + x2 = 0 + 11.17769856 Combine like terms: -11.17769856 + 11.17769856 = 0.00000000 0.00000000 + 0.02520720829x + x2 = 0 + 11.17769856 0.02520720829x + x2 = 0 + 11.17769856 Combine like terms: 0 + 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 = 3.33072668285 x = 3.33072668285 Simplifying x = 3.33072668285Subproblem 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 = -3.35593389115 x = -3.35593389115 Simplifying x = -3.35593389115Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.33072668285, -3.35593389115}
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