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Simplifying 0.3x + -60 = 2.4x + -0.001x2 Reorder the terms: -60 + 0.3x = 2.4x + -0.001x2 Solving -60 + 0.3x = 2.4x + -0.001x2 Solving for variable 'x'. Combine like terms: 0.3x + -2.4x = -2.1x -60 + -2.1x + 0.001x2 = 2.4x + -0.001x2 + -2.4x + 0.001x2 Reorder the terms: -60 + -2.1x + 0.001x2 = 2.4x + -2.4x + -0.001x2 + 0.001x2 Combine like terms: 2.4x + -2.4x = 0.0 -60 + -2.1x + 0.001x2 = 0.0 + -0.001x2 + 0.001x2 -60 + -2.1x + 0.001x2 = -0.001x2 + 0.001x2 Combine like terms: -0.001x2 + 0.001x2 = 0.000 -60 + -2.1x + 0.001x2 = 0.000 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. -60000 + -2100x + x2 = 0 Move the constant term to the right: Add '60000' to each side of the equation. -60000 + -2100x + 60000 + x2 = 0 + 60000 Reorder the terms: -60000 + 60000 + -2100x + x2 = 0 + 60000 Combine like terms: -60000 + 60000 = 0 0 + -2100x + x2 = 0 + 60000 -2100x + x2 = 0 + 60000 Combine like terms: 0 + 60000 = 60000 -2100x + x2 = 60000 The x term is -2100x. Take half its coefficient (-1050). Square it (1102500) and add it to both sides. Add '1102500' to each side of the equation. -2100x + 1102500 + x2 = 60000 + 1102500 Reorder the terms: 1102500 + -2100x + x2 = 60000 + 1102500 Combine like terms: 60000 + 1102500 = 1162500 1102500 + -2100x + x2 = 1162500 Factor a perfect square on the left side: (x + -1050)(x + -1050) = 1162500 Calculate the square root of the right side: 1078.192932642 Break this problem into two subproblems by setting (x + -1050) equal to 1078.192932642 and -1078.192932642.Subproblem 1
x + -1050 = 1078.192932642 Simplifying x + -1050 = 1078.192932642 Reorder the terms: -1050 + x = 1078.192932642 Solving -1050 + x = 1078.192932642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1050' to each side of the equation. -1050 + 1050 + x = 1078.192932642 + 1050 Combine like terms: -1050 + 1050 = 0 0 + x = 1078.192932642 + 1050 x = 1078.192932642 + 1050 Combine like terms: 1078.192932642 + 1050 = 2128.192932642 x = 2128.192932642 Simplifying x = 2128.192932642Subproblem 2
x + -1050 = -1078.192932642 Simplifying x + -1050 = -1078.192932642 Reorder the terms: -1050 + x = -1078.192932642 Solving -1050 + x = -1078.192932642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1050' to each side of the equation. -1050 + 1050 + x = -1078.192932642 + 1050 Combine like terms: -1050 + 1050 = 0 0 + x = -1078.192932642 + 1050 x = -1078.192932642 + 1050 Combine like terms: -1078.192932642 + 1050 = -28.192932642 x = -28.192932642 Simplifying x = -28.192932642Solution
The solution to the problem is based on the solutions from the subproblems. x = {2128.192932642, -28.192932642}
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