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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 = 31.26044347829 31.23523627 + 11.17769856x + x2 = 31.26044347829 Factor a perfect square on the left side: (x + 5.58884928)(x + 5.58884928) = 31.26044347829 Calculate the square root of the right side: 5.591103959 Break this problem into two subproblems by setting (x + 5.58884928) equal to 5.591103959 and -5.591103959.Subproblem 1
x + 5.58884928 = 5.591103959 Simplifying x + 5.58884928 = 5.591103959 Reorder the terms: 5.58884928 + x = 5.591103959 Solving 5.58884928 + x = 5.591103959 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 = 5.591103959 + -5.58884928 Combine like terms: 5.58884928 + -5.58884928 = 0.00000000 0.00000000 + x = 5.591103959 + -5.58884928 x = 5.591103959 + -5.58884928 Combine like terms: 5.591103959 + -5.58884928 = 0.002254679 x = 0.002254679 Simplifying x = 0.002254679Subproblem 2
x + 5.58884928 = -5.591103959 Simplifying x + 5.58884928 = -5.591103959 Reorder the terms: 5.58884928 + x = -5.591103959 Solving 5.58884928 + x = -5.591103959 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 = -5.591103959 + -5.58884928 Combine like terms: 5.58884928 + -5.58884928 = 0.00000000 0.00000000 + x = -5.591103959 + -5.58884928 x = -5.591103959 + -5.58884928 Combine like terms: -5.591103959 + -5.58884928 = -11.179953239 x = -11.179953239 Simplifying x = -11.179953239Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.002254679, -11.179953239}
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