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Simplifying 3209.08649133359 + -2560.04269436112x + -4890.04107030911x2 = 0 Solving 3209.08649133359 + -2560.04269436112x + -4890.04107030911x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4890.04107030911 the coefficient of the squared term: Divide each side by '-4890.04107030911'. -0.6562493945 + 0.5235217164x + x2 = 0 Move the constant term to the right: Add '0.6562493945' to each side of the equation. -0.6562493945 + 0.5235217164x + 0.6562493945 + x2 = 0 + 0.6562493945 Reorder the terms: -0.6562493945 + 0.6562493945 + 0.5235217164x + x2 = 0 + 0.6562493945 Combine like terms: -0.6562493945 + 0.6562493945 = 0.0000000000 0.0000000000 + 0.5235217164x + x2 = 0 + 0.6562493945 0.5235217164x + x2 = 0 + 0.6562493945 Combine like terms: 0 + 0.6562493945 = 0.6562493945 0.5235217164x + x2 = 0.6562493945 The x term is 0.5235217164x. Take half its coefficient (0.2617608582). Square it (0.06851874689) and add it to both sides. Add '0.06851874689' to each side of the equation. 0.5235217164x + 0.06851874689 + x2 = 0.6562493945 + 0.06851874689 Reorder the terms: 0.06851874689 + 0.5235217164x + x2 = 0.6562493945 + 0.06851874689 Combine like terms: 0.6562493945 + 0.06851874689 = 0.72476814139 0.06851874689 + 0.5235217164x + x2 = 0.72476814139 Factor a perfect square on the left side: (x + 0.2617608582)(x + 0.2617608582) = 0.72476814139 Calculate the square root of the right side: 0.851333155 Break this problem into two subproblems by setting (x + 0.2617608582) equal to 0.851333155 and -0.851333155.Subproblem 1
x + 0.2617608582 = 0.851333155 Simplifying x + 0.2617608582 = 0.851333155 Reorder the terms: 0.2617608582 + x = 0.851333155 Solving 0.2617608582 + x = 0.851333155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2617608582' to each side of the equation. 0.2617608582 + -0.2617608582 + x = 0.851333155 + -0.2617608582 Combine like terms: 0.2617608582 + -0.2617608582 = 0.0000000000 0.0000000000 + x = 0.851333155 + -0.2617608582 x = 0.851333155 + -0.2617608582 Combine like terms: 0.851333155 + -0.2617608582 = 0.5895722968 x = 0.5895722968 Simplifying x = 0.5895722968Subproblem 2
x + 0.2617608582 = -0.851333155 Simplifying x + 0.2617608582 = -0.851333155 Reorder the terms: 0.2617608582 + x = -0.851333155 Solving 0.2617608582 + x = -0.851333155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2617608582' to each side of the equation. 0.2617608582 + -0.2617608582 + x = -0.851333155 + -0.2617608582 Combine like terms: 0.2617608582 + -0.2617608582 = 0.0000000000 0.0000000000 + x = -0.851333155 + -0.2617608582 x = -0.851333155 + -0.2617608582 Combine like terms: -0.851333155 + -0.2617608582 = -1.1130940132 x = -1.1130940132 Simplifying x = -1.1130940132Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5895722968, -1.1130940132}
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