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Simplifying 1760 + 8x + 0.6x2 = 100x + -0.4x2 Solving 1760 + 8x + 0.6x2 = 100x + -0.4x2 Solving for variable 'x'. Reorder the terms: 1760 + 8x + -100x + 0.6x2 + 0.4x2 = 100x + -0.4x2 + -100x + 0.4x2 Combine like terms: 8x + -100x = -92x 1760 + -92x + 0.6x2 + 0.4x2 = 100x + -0.4x2 + -100x + 0.4x2 Combine like terms: 0.6x2 + 0.4x2 = 1x2 1760 + -92x + 1x2 = 100x + -0.4x2 + -100x + 0.4x2 Reorder the terms: 1760 + -92x + 1x2 = 100x + -100x + -0.4x2 + 0.4x2 Combine like terms: 100x + -100x = 0 1760 + -92x + 1x2 = 0 + -0.4x2 + 0.4x2 1760 + -92x + 1x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 1760 + -92x + 1x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-1760' to each side of the equation. 1760 + -92x + -1760 + x2 = 0.0 + -1760 Reorder the terms: 1760 + -1760 + -92x + x2 = 0.0 + -1760 Combine like terms: 1760 + -1760 = 0 0 + -92x + x2 = 0.0 + -1760 -92x + x2 = 0.0 + -1760 Combine like terms: 0.0 + -1760 = -1760 -92x + x2 = -1760 The x term is -92x. Take half its coefficient (-46). Square it (2116) and add it to both sides. Add '2116' to each side of the equation. -92x + 2116 + x2 = -1760 + 2116 Reorder the terms: 2116 + -92x + x2 = -1760 + 2116 Combine like terms: -1760 + 2116 = 356 2116 + -92x + x2 = 356 Factor a perfect square on the left side: (x + -46)(x + -46) = 356 Calculate the square root of the right side: 18.867962264 Break this problem into two subproblems by setting (x + -46) equal to 18.867962264 and -18.867962264.Subproblem 1
x + -46 = 18.867962264 Simplifying x + -46 = 18.867962264 Reorder the terms: -46 + x = 18.867962264 Solving -46 + x = 18.867962264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46' to each side of the equation. -46 + 46 + x = 18.867962264 + 46 Combine like terms: -46 + 46 = 0 0 + x = 18.867962264 + 46 x = 18.867962264 + 46 Combine like terms: 18.867962264 + 46 = 64.867962264 x = 64.867962264 Simplifying x = 64.867962264Subproblem 2
x + -46 = -18.867962264 Simplifying x + -46 = -18.867962264 Reorder the terms: -46 + x = -18.867962264 Solving -46 + x = -18.867962264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46' to each side of the equation. -46 + 46 + x = -18.867962264 + 46 Combine like terms: -46 + 46 = 0 0 + x = -18.867962264 + 46 x = -18.867962264 + 46 Combine like terms: -18.867962264 + 46 = 27.132037736 x = 27.132037736 Simplifying x = 27.132037736Solution
The solution to the problem is based on the solutions from the subproblems. x = {64.867962264, 27.132037736}
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