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Simplifying 124x + -0.1x2 = -2950 Solving 124x + -0.1x2 = -2950 Solving for variable 'x'. Reorder the terms: 2950 + 124x + -0.1x2 = -2950 + 2950 Combine like terms: -2950 + 2950 = 0 2950 + 124x + -0.1x2 = 0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -29500 + -1240x + x2 = 0 Move the constant term to the right: Add '29500' to each side of the equation. -29500 + -1240x + 29500 + x2 = 0 + 29500 Reorder the terms: -29500 + 29500 + -1240x + x2 = 0 + 29500 Combine like terms: -29500 + 29500 = 0 0 + -1240x + x2 = 0 + 29500 -1240x + x2 = 0 + 29500 Combine like terms: 0 + 29500 = 29500 -1240x + x2 = 29500 The x term is -1240x. Take half its coefficient (-620). Square it (384400) and add it to both sides. Add '384400' to each side of the equation. -1240x + 384400 + x2 = 29500 + 384400 Reorder the terms: 384400 + -1240x + x2 = 29500 + 384400 Combine like terms: 29500 + 384400 = 413900 384400 + -1240x + x2 = 413900 Factor a perfect square on the left side: (x + -620)(x + -620) = 413900 Calculate the square root of the right side: 643.350604259 Break this problem into two subproblems by setting (x + -620) equal to 643.350604259 and -643.350604259.Subproblem 1
x + -620 = 643.350604259 Simplifying x + -620 = 643.350604259 Reorder the terms: -620 + x = 643.350604259 Solving -620 + x = 643.350604259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '620' to each side of the equation. -620 + 620 + x = 643.350604259 + 620 Combine like terms: -620 + 620 = 0 0 + x = 643.350604259 + 620 x = 643.350604259 + 620 Combine like terms: 643.350604259 + 620 = 1263.350604259 x = 1263.350604259 Simplifying x = 1263.350604259Subproblem 2
x + -620 = -643.350604259 Simplifying x + -620 = -643.350604259 Reorder the terms: -620 + x = -643.350604259 Solving -620 + x = -643.350604259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '620' to each side of the equation. -620 + 620 + x = -643.350604259 + 620 Combine like terms: -620 + 620 = 0 0 + x = -643.350604259 + 620 x = -643.350604259 + 620 Combine like terms: -643.350604259 + 620 = -23.350604259 x = -23.350604259 Simplifying x = -23.350604259Solution
The solution to the problem is based on the solutions from the subproblems. x = {1263.350604259, -23.350604259}
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