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Simplifying 124x + -0.1x2 = 2850 Solving 124x + -0.1x2 = 2850 Solving for variable 'x'. Reorder the terms: -2850 + 124x + -0.1x2 = 2850 + -2850 Combine like terms: 2850 + -2850 = 0 -2850 + 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'. 28500 + -1240x + x2 = 0 Move the constant term to the right: Add '-28500' to each side of the equation. 28500 + -1240x + -28500 + x2 = 0 + -28500 Reorder the terms: 28500 + -28500 + -1240x + x2 = 0 + -28500 Combine like terms: 28500 + -28500 = 0 0 + -1240x + x2 = 0 + -28500 -1240x + x2 = 0 + -28500 Combine like terms: 0 + -28500 = -28500 -1240x + x2 = -28500 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 = -28500 + 384400 Reorder the terms: 384400 + -1240x + x2 = -28500 + 384400 Combine like terms: -28500 + 384400 = 355900 384400 + -1240x + x2 = 355900 Factor a perfect square on the left side: (x + -620)(x + -620) = 355900 Calculate the square root of the right side: 596.573549531 Break this problem into two subproblems by setting (x + -620) equal to 596.573549531 and -596.573549531.Subproblem 1
x + -620 = 596.573549531 Simplifying x + -620 = 596.573549531 Reorder the terms: -620 + x = 596.573549531 Solving -620 + x = 596.573549531 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 = 596.573549531 + 620 Combine like terms: -620 + 620 = 0 0 + x = 596.573549531 + 620 x = 596.573549531 + 620 Combine like terms: 596.573549531 + 620 = 1216.573549531 x = 1216.573549531 Simplifying x = 1216.573549531Subproblem 2
x + -620 = -596.573549531 Simplifying x + -620 = -596.573549531 Reorder the terms: -620 + x = -596.573549531 Solving -620 + x = -596.573549531 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 = -596.573549531 + 620 Combine like terms: -620 + 620 = 0 0 + x = -596.573549531 + 620 x = -596.573549531 + 620 Combine like terms: -596.573549531 + 620 = 23.426450469 x = 23.426450469 Simplifying x = 23.426450469Solution
The solution to the problem is based on the solutions from the subproblems. x = {1216.573549531, 23.426450469}
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