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Simplifying 0.03x2 + -6000x + 98990 = 0 Reorder the terms: 98990 + -6000x + 0.03x2 = 0 Solving 98990 + -6000x + 0.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 3299666.667 + -200000x + x2 = 0 Move the constant term to the right: Add '-3299666.667' to each side of the equation. 3299666.667 + -200000x + -3299666.667 + x2 = 0 + -3299666.667 Reorder the terms: 3299666.667 + -3299666.667 + -200000x + x2 = 0 + -3299666.667 Combine like terms: 3299666.667 + -3299666.667 = 0.000 0.000 + -200000x + x2 = 0 + -3299666.667 -200000x + x2 = 0 + -3299666.667 Combine like terms: 0 + -3299666.667 = -3299666.667 -200000x + x2 = -3299666.667 The x term is -200000x. Take half its coefficient (-100000). Square it (10000000000) and add it to both sides. Add '10000000000' to each side of the equation. -200000x + 10000000000 + x2 = -3299666.667 + 10000000000 Reorder the terms: 10000000000 + -200000x + x2 = -3299666.667 + 10000000000 Combine like terms: -3299666.667 + 10000000000 = 9996700333.333 10000000000 + -200000x + x2 = 9996700333.333 Factor a perfect square on the left side: (x + -100000)(x + -100000) = 9996700333.333 Calculate the square root of the right side: 99983.500305465 Break this problem into two subproblems by setting (x + -100000) equal to 99983.500305465 and -99983.500305465.Subproblem 1
x + -100000 = 99983.500305465 Simplifying x + -100000 = 99983.500305465 Reorder the terms: -100000 + x = 99983.500305465 Solving -100000 + x = 99983.500305465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100000' to each side of the equation. -100000 + 100000 + x = 99983.500305465 + 100000 Combine like terms: -100000 + 100000 = 0 0 + x = 99983.500305465 + 100000 x = 99983.500305465 + 100000 Combine like terms: 99983.500305465 + 100000 = 199983.500305465 x = 199983.500305465 Simplifying x = 199983.500305465Subproblem 2
x + -100000 = -99983.500305465 Simplifying x + -100000 = -99983.500305465 Reorder the terms: -100000 + x = -99983.500305465 Solving -100000 + x = -99983.500305465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100000' to each side of the equation. -100000 + 100000 + x = -99983.500305465 + 100000 Combine like terms: -100000 + 100000 = 0 0 + x = -99983.500305465 + 100000 x = -99983.500305465 + 100000 Combine like terms: -99983.500305465 + 100000 = 16.499694535 x = 16.499694535 Simplifying x = 16.499694535Solution
The solution to the problem is based on the solutions from the subproblems. x = {199983.500305465, 16.499694535}
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