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Simplifying 2x2 + -3x + -1000 = 0 Reorder the terms: -1000 + -3x + 2x2 = 0 Solving -1000 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -500 + -1.5x + x2 = 0 Move the constant term to the right: Add '500' to each side of the equation. -500 + -1.5x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -1.5x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -1.5x + x2 = 0 + 500 -1.5x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -1.5x + x2 = 500 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 500 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 500 + 0.5625 Combine like terms: 500 + 0.5625 = 500.5625 0.5625 + -1.5x + x2 = 500.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 500.5625 Calculate the square root of the right side: 22.373254122 Break this problem into two subproblems by setting (x + -0.75) equal to 22.373254122 and -22.373254122.Subproblem 1
x + -0.75 = 22.373254122 Simplifying x + -0.75 = 22.373254122 Reorder the terms: -0.75 + x = 22.373254122 Solving -0.75 + x = 22.373254122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 22.373254122 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 22.373254122 + 0.75 x = 22.373254122 + 0.75 Combine like terms: 22.373254122 + 0.75 = 23.123254122 x = 23.123254122 Simplifying x = 23.123254122Subproblem 2
x + -0.75 = -22.373254122 Simplifying x + -0.75 = -22.373254122 Reorder the terms: -0.75 + x = -22.373254122 Solving -0.75 + x = -22.373254122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -22.373254122 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -22.373254122 + 0.75 x = -22.373254122 + 0.75 Combine like terms: -22.373254122 + 0.75 = -21.623254122 x = -21.623254122 Simplifying x = -21.623254122Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.123254122, -21.623254122}
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