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Simplifying 2720.38144853333 + -2485.78848747977x + -4972.54574462172x2 = 0 Solving 2720.38144853333 + -2485.78848747977x + -4972.54574462172x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4972.54574462172 the coefficient of the squared term: Divide each side by '-4972.54574462172'. -0.5470802258 + 0.4999025882x + x2 = 0 Move the constant term to the right: Add '0.5470802258' to each side of the equation. -0.5470802258 + 0.4999025882x + 0.5470802258 + x2 = 0 + 0.5470802258 Reorder the terms: -0.5470802258 + 0.5470802258 + 0.4999025882x + x2 = 0 + 0.5470802258 Combine like terms: -0.5470802258 + 0.5470802258 = 0.0000000000 0.0000000000 + 0.4999025882x + x2 = 0 + 0.5470802258 0.4999025882x + x2 = 0 + 0.5470802258 Combine like terms: 0 + 0.5470802258 = 0.5470802258 0.4999025882x + x2 = 0.5470802258 The x term is 0.4999025882x. Take half its coefficient (0.2499512941). Square it (0.06247564942) and add it to both sides. Add '0.06247564942' to each side of the equation. 0.4999025882x + 0.06247564942 + x2 = 0.5470802258 + 0.06247564942 Reorder the terms: 0.06247564942 + 0.4999025882x + x2 = 0.5470802258 + 0.06247564942 Combine like terms: 0.5470802258 + 0.06247564942 = 0.60955587522 0.06247564942 + 0.4999025882x + x2 = 0.60955587522 Factor a perfect square on the left side: (x + 0.2499512941)(x + 0.2499512941) = 0.60955587522 Calculate the square root of the right side: 0.780740594 Break this problem into two subproblems by setting (x + 0.2499512941) equal to 0.780740594 and -0.780740594.Subproblem 1
x + 0.2499512941 = 0.780740594 Simplifying x + 0.2499512941 = 0.780740594 Reorder the terms: 0.2499512941 + x = 0.780740594 Solving 0.2499512941 + x = 0.780740594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2499512941' to each side of the equation. 0.2499512941 + -0.2499512941 + x = 0.780740594 + -0.2499512941 Combine like terms: 0.2499512941 + -0.2499512941 = 0.0000000000 0.0000000000 + x = 0.780740594 + -0.2499512941 x = 0.780740594 + -0.2499512941 Combine like terms: 0.780740594 + -0.2499512941 = 0.5307892999 x = 0.5307892999 Simplifying x = 0.5307892999Subproblem 2
x + 0.2499512941 = -0.780740594 Simplifying x + 0.2499512941 = -0.780740594 Reorder the terms: 0.2499512941 + x = -0.780740594 Solving 0.2499512941 + x = -0.780740594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2499512941' to each side of the equation. 0.2499512941 + -0.2499512941 + x = -0.780740594 + -0.2499512941 Combine like terms: 0.2499512941 + -0.2499512941 = 0.0000000000 0.0000000000 + x = -0.780740594 + -0.2499512941 x = -0.780740594 + -0.2499512941 Combine like terms: -0.780740594 + -0.2499512941 = -1.0306918881 x = -1.0306918881 Simplifying x = -1.0306918881Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5307892999, -1.0306918881}
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