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Simplifying -0.018x2 + 1.656x + 4.4 = 0 Reorder the terms: 4.4 + 1.656x + -0.018x2 = 0 Solving 4.4 + 1.656x + -0.018x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.018 the coefficient of the squared term: Divide each side by '-0.018'. -244.4444444 + -92x + x2 = 0 Move the constant term to the right: Add '244.4444444' to each side of the equation. -244.4444444 + -92x + 244.4444444 + x2 = 0 + 244.4444444 Reorder the terms: -244.4444444 + 244.4444444 + -92x + x2 = 0 + 244.4444444 Combine like terms: -244.4444444 + 244.4444444 = 0.0000000 0.0000000 + -92x + x2 = 0 + 244.4444444 -92x + x2 = 0 + 244.4444444 Combine like terms: 0 + 244.4444444 = 244.4444444 -92x + x2 = 244.4444444 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 = 244.4444444 + 2116 Reorder the terms: 2116 + -92x + x2 = 244.4444444 + 2116 Combine like terms: 244.4444444 + 2116 = 2360.4444444 2116 + -92x + x2 = 2360.4444444 Factor a perfect square on the left side: (x + -46)(x + -46) = 2360.4444444 Calculate the square root of the right side: 48.584405362 Break this problem into two subproblems by setting (x + -46) equal to 48.584405362 and -48.584405362.Subproblem 1
x + -46 = 48.584405362 Simplifying x + -46 = 48.584405362 Reorder the terms: -46 + x = 48.584405362 Solving -46 + x = 48.584405362 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 = 48.584405362 + 46 Combine like terms: -46 + 46 = 0 0 + x = 48.584405362 + 46 x = 48.584405362 + 46 Combine like terms: 48.584405362 + 46 = 94.584405362 x = 94.584405362 Simplifying x = 94.584405362Subproblem 2
x + -46 = -48.584405362 Simplifying x + -46 = -48.584405362 Reorder the terms: -46 + x = -48.584405362 Solving -46 + x = -48.584405362 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 = -48.584405362 + 46 Combine like terms: -46 + 46 = 0 0 + x = -48.584405362 + 46 x = -48.584405362 + 46 Combine like terms: -48.584405362 + 46 = -2.584405362 x = -2.584405362 Simplifying x = -2.584405362Solution
The solution to the problem is based on the solutions from the subproblems. x = {94.584405362, -2.584405362}
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