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Simplifying 30x2 + -1001 * 1001x + -1001 = 0 Multiply -1001 * 1001 30x2 + -1002001x + -1001 = 0 Reorder the terms: -1001 + -1002001x + 30x2 = 0 Solving -1001 + -1002001x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -33.36666667 + -33400.03333x + x2 = 0 Move the constant term to the right: Add '33.36666667' to each side of the equation. -33.36666667 + -33400.03333x + 33.36666667 + x2 = 0 + 33.36666667 Reorder the terms: -33.36666667 + 33.36666667 + -33400.03333x + x2 = 0 + 33.36666667 Combine like terms: -33.36666667 + 33.36666667 = 0.00000000 0.00000000 + -33400.03333x + x2 = 0 + 33.36666667 -33400.03333x + x2 = 0 + 33.36666667 Combine like terms: 0 + 33.36666667 = 33.36666667 -33400.03333x + x2 = 33.36666667 The x term is -33400.03333x. Take half its coefficient (-16700.01667). Square it (278890556.8) and add it to both sides. Add '278890556.8' to each side of the equation. -33400.03333x + 278890556.8 + x2 = 33.36666667 + 278890556.8 Reorder the terms: 278890556.8 + -33400.03333x + x2 = 33.36666667 + 278890556.8 Combine like terms: 33.36666667 + 278890556.8 = 278890590.16666667 278890556.8 + -33400.03333x + x2 = 278890590.16666667 Factor a perfect square on the left side: (x + -16700.01667)(x + -16700.01667) = 278890590.16666667 Calculate the square root of the right side: 16700.017669651 Break this problem into two subproblems by setting (x + -16700.01667) equal to 16700.017669651 and -16700.017669651.Subproblem 1
x + -16700.01667 = 16700.017669651 Simplifying x + -16700.01667 = 16700.017669651 Reorder the terms: -16700.01667 + x = 16700.017669651 Solving -16700.01667 + x = 16700.017669651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16700.01667' to each side of the equation. -16700.01667 + 16700.01667 + x = 16700.017669651 + 16700.01667 Combine like terms: -16700.01667 + 16700.01667 = 0.00000 0.00000 + x = 16700.017669651 + 16700.01667 x = 16700.017669651 + 16700.01667 Combine like terms: 16700.017669651 + 16700.01667 = 33400.034339651 x = 33400.034339651 Simplifying x = 33400.034339651Subproblem 2
x + -16700.01667 = -16700.017669651 Simplifying x + -16700.01667 = -16700.017669651 Reorder the terms: -16700.01667 + x = -16700.017669651 Solving -16700.01667 + x = -16700.017669651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16700.01667' to each side of the equation. -16700.01667 + 16700.01667 + x = -16700.017669651 + 16700.01667 Combine like terms: -16700.01667 + 16700.01667 = 0.00000 0.00000 + x = -16700.017669651 + 16700.01667 x = -16700.017669651 + 16700.01667 Combine like terms: -16700.017669651 + 16700.01667 = -0.000999651 x = -0.000999651 Simplifying x = -0.000999651Solution
The solution to the problem is based on the solutions from the subproblems. x = {33400.034339651, -0.000999651}
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