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Simplifying 3221.56997094199 + -2503.86703612331x + -4952.45846835113x2 = 0 Solving 3221.56997094199 + -2503.86703612331x + -4952.45846835113x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4952.45846835113 the coefficient of the squared term: Divide each side by '-4952.45846835113'. -0.6504991393 + 0.5055806227x + x2 = 0 Move the constant term to the right: Add '0.6504991393' to each side of the equation. -0.6504991393 + 0.5055806227x + 0.6504991393 + x2 = 0 + 0.6504991393 Reorder the terms: -0.6504991393 + 0.6504991393 + 0.5055806227x + x2 = 0 + 0.6504991393 Combine like terms: -0.6504991393 + 0.6504991393 = 0.0000000000 0.0000000000 + 0.5055806227x + x2 = 0 + 0.6504991393 0.5055806227x + x2 = 0 + 0.6504991393 Combine like terms: 0 + 0.6504991393 = 0.6504991393 0.5055806227x + x2 = 0.6504991393 The x term is 0.5055806227x. Take half its coefficient (0.2527903114). Square it (0.06390294154) and add it to both sides. Add '0.06390294154' to each side of the equation. 0.5055806227x + 0.06390294154 + x2 = 0.6504991393 + 0.06390294154 Reorder the terms: 0.06390294154 + 0.5055806227x + x2 = 0.6504991393 + 0.06390294154 Combine like terms: 0.6504991393 + 0.06390294154 = 0.71440208084 0.06390294154 + 0.5055806227x + x2 = 0.71440208084 Factor a perfect square on the left side: (x + 0.2527903114)(x + 0.2527903114) = 0.71440208084 Calculate the square root of the right side: 0.845223095 Break this problem into two subproblems by setting (x + 0.2527903114) equal to 0.845223095 and -0.845223095.Subproblem 1
x + 0.2527903114 = 0.845223095 Simplifying x + 0.2527903114 = 0.845223095 Reorder the terms: 0.2527903114 + x = 0.845223095 Solving 0.2527903114 + x = 0.845223095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2527903114' to each side of the equation. 0.2527903114 + -0.2527903114 + x = 0.845223095 + -0.2527903114 Combine like terms: 0.2527903114 + -0.2527903114 = 0.0000000000 0.0000000000 + x = 0.845223095 + -0.2527903114 x = 0.845223095 + -0.2527903114 Combine like terms: 0.845223095 + -0.2527903114 = 0.5924327836 x = 0.5924327836 Simplifying x = 0.5924327836Subproblem 2
x + 0.2527903114 = -0.845223095 Simplifying x + 0.2527903114 = -0.845223095 Reorder the terms: 0.2527903114 + x = -0.845223095 Solving 0.2527903114 + x = -0.845223095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2527903114' to each side of the equation. 0.2527903114 + -0.2527903114 + x = -0.845223095 + -0.2527903114 Combine like terms: 0.2527903114 + -0.2527903114 = 0.0000000000 0.0000000000 + x = -0.845223095 + -0.2527903114 x = -0.845223095 + -0.2527903114 Combine like terms: -0.845223095 + -0.2527903114 = -1.0980134064 x = -1.0980134064 Simplifying x = -1.0980134064Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5924327836, -1.0980134064}
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