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Simplifying 83.3x2 + -42.2x + 5.08 = 0 Reorder the terms: 5.08 + -42.2x + 83.3x2 = 0 Solving 5.08 + -42.2x + 83.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 83.3 the coefficient of the squared term: Divide each side by '83.3'. 0.06098439376 + -0.5066026411x + x2 = 0 Move the constant term to the right: Add '-0.06098439376' to each side of the equation. 0.06098439376 + -0.5066026411x + -0.06098439376 + x2 = 0 + -0.06098439376 Reorder the terms: 0.06098439376 + -0.06098439376 + -0.5066026411x + x2 = 0 + -0.06098439376 Combine like terms: 0.06098439376 + -0.06098439376 = 0.00000000000 0.00000000000 + -0.5066026411x + x2 = 0 + -0.06098439376 -0.5066026411x + x2 = 0 + -0.06098439376 Combine like terms: 0 + -0.06098439376 = -0.06098439376 -0.5066026411x + x2 = -0.06098439376 The x term is -0.5066026411x. Take half its coefficient (-0.2533013206). Square it (0.06416155902) and add it to both sides. Add '0.06416155902' to each side of the equation. -0.5066026411x + 0.06416155902 + x2 = -0.06098439376 + 0.06416155902 Reorder the terms: 0.06416155902 + -0.5066026411x + x2 = -0.06098439376 + 0.06416155902 Combine like terms: -0.06098439376 + 0.06416155902 = 0.00317716526 0.06416155902 + -0.5066026411x + x2 = 0.00317716526 Factor a perfect square on the left side: (x + -0.2533013206)(x + -0.2533013206) = 0.00317716526 Calculate the square root of the right side: 0.056366349 Break this problem into two subproblems by setting (x + -0.2533013206) equal to 0.056366349 and -0.056366349.Subproblem 1
x + -0.2533013206 = 0.056366349 Simplifying x + -0.2533013206 = 0.056366349 Reorder the terms: -0.2533013206 + x = 0.056366349 Solving -0.2533013206 + x = 0.056366349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2533013206' to each side of the equation. -0.2533013206 + 0.2533013206 + x = 0.056366349 + 0.2533013206 Combine like terms: -0.2533013206 + 0.2533013206 = 0.0000000000 0.0000000000 + x = 0.056366349 + 0.2533013206 x = 0.056366349 + 0.2533013206 Combine like terms: 0.056366349 + 0.2533013206 = 0.3096676696 x = 0.3096676696 Simplifying x = 0.3096676696Subproblem 2
x + -0.2533013206 = -0.056366349 Simplifying x + -0.2533013206 = -0.056366349 Reorder the terms: -0.2533013206 + x = -0.056366349 Solving -0.2533013206 + x = -0.056366349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2533013206' to each side of the equation. -0.2533013206 + 0.2533013206 + x = -0.056366349 + 0.2533013206 Combine like terms: -0.2533013206 + 0.2533013206 = 0.0000000000 0.0000000000 + x = -0.056366349 + 0.2533013206 x = -0.056366349 + 0.2533013206 Combine like terms: -0.056366349 + 0.2533013206 = 0.1969349716 x = 0.1969349716 Simplifying x = 0.1969349716Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3096676696, 0.1969349716}
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