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Simplifying -39.671192x2 + 443.432625675216x + -1 = 0 Reorder the terms: -1 + 443.432625675216x + -39.671192x2 = 0 Solving -1 + 443.432625675216x + -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'. 0.02520720829 + -11.17769856x + x2 = 0 Move the constant term to the right: Add '-0.02520720829' to each side of the equation. 0.02520720829 + -11.17769856x + -0.02520720829 + x2 = 0 + -0.02520720829 Reorder the terms: 0.02520720829 + -0.02520720829 + -11.17769856x + x2 = 0 + -0.02520720829 Combine like terms: 0.02520720829 + -0.02520720829 = 0.00000000000 0.00000000000 + -11.17769856x + x2 = 0 + -0.02520720829 -11.17769856x + x2 = 0 + -0.02520720829 Combine like terms: 0 + -0.02520720829 = -0.02520720829 -11.17769856x + x2 = -0.02520720829 The x term is -11.17769856x. Take half its coefficient (-5.58884928). Square it (31.23523627) and add it to both sides. Add '31.23523627' to each side of the equation. -11.17769856x + 31.23523627 + x2 = -0.02520720829 + 31.23523627 Reorder the terms: 31.23523627 + -11.17769856x + x2 = -0.02520720829 + 31.23523627 Combine like terms: -0.02520720829 + 31.23523627 = 31.21002906171 31.23523627 + -11.17769856x + x2 = 31.21002906171 Factor a perfect square on the left side: (x + -5.58884928)(x + -5.58884928) = 31.21002906171 Calculate the square root of the right side: 5.58659369 Break this problem into two subproblems by setting (x + -5.58884928) equal to 5.58659369 and -5.58659369.Subproblem 1
x + -5.58884928 = 5.58659369 Simplifying x + -5.58884928 = 5.58659369 Reorder the terms: -5.58884928 + x = 5.58659369 Solving -5.58884928 + x = 5.58659369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.58884928' to each side of the equation. -5.58884928 + 5.58884928 + x = 5.58659369 + 5.58884928 Combine like terms: -5.58884928 + 5.58884928 = 0.00000000 0.00000000 + x = 5.58659369 + 5.58884928 x = 5.58659369 + 5.58884928 Combine like terms: 5.58659369 + 5.58884928 = 11.17544297 x = 11.17544297 Simplifying x = 11.17544297Subproblem 2
x + -5.58884928 = -5.58659369 Simplifying x + -5.58884928 = -5.58659369 Reorder the terms: -5.58884928 + x = -5.58659369 Solving -5.58884928 + x = -5.58659369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.58884928' to each side of the equation. -5.58884928 + 5.58884928 + x = -5.58659369 + 5.58884928 Combine like terms: -5.58884928 + 5.58884928 = 0.00000000 0.00000000 + x = -5.58659369 + 5.58884928 x = -5.58659369 + 5.58884928 Combine like terms: -5.58659369 + 5.58884928 = 0.00225559 x = 0.00225559 Simplifying x = 0.00225559Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.17544297, 0.00225559}
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