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Simplifying -24x2 + 9.33x + -0.83 = 0 Reorder the terms: -0.83 + 9.33x + -24x2 = 0 Solving -0.83 + 9.33x + -24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. 0.03458333333 + -0.38875x + x2 = 0 Move the constant term to the right: Add '-0.03458333333' to each side of the equation. 0.03458333333 + -0.38875x + -0.03458333333 + x2 = 0 + -0.03458333333 Reorder the terms: 0.03458333333 + -0.03458333333 + -0.38875x + x2 = 0 + -0.03458333333 Combine like terms: 0.03458333333 + -0.03458333333 = 0.00000000000 0.00000000000 + -0.38875x + x2 = 0 + -0.03458333333 -0.38875x + x2 = 0 + -0.03458333333 Combine like terms: 0 + -0.03458333333 = -0.03458333333 -0.38875x + x2 = -0.03458333333 The x term is -0.38875x. Take half its coefficient (-0.194375). Square it (0.03778164063) and add it to both sides. Add '0.03778164063' to each side of the equation. -0.38875x + 0.03778164063 + x2 = -0.03458333333 + 0.03778164063 Reorder the terms: 0.03778164063 + -0.38875x + x2 = -0.03458333333 + 0.03778164063 Combine like terms: -0.03458333333 + 0.03778164063 = 0.0031983073 0.03778164063 + -0.38875x + x2 = 0.0031983073 Factor a perfect square on the left side: (x + -0.194375)(x + -0.194375) = 0.0031983073 Calculate the square root of the right side: 0.056553579 Break this problem into two subproblems by setting (x + -0.194375) equal to 0.056553579 and -0.056553579.Subproblem 1
x + -0.194375 = 0.056553579 Simplifying x + -0.194375 = 0.056553579 Reorder the terms: -0.194375 + x = 0.056553579 Solving -0.194375 + x = 0.056553579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.194375' to each side of the equation. -0.194375 + 0.194375 + x = 0.056553579 + 0.194375 Combine like terms: -0.194375 + 0.194375 = 0.000000 0.000000 + x = 0.056553579 + 0.194375 x = 0.056553579 + 0.194375 Combine like terms: 0.056553579 + 0.194375 = 0.250928579 x = 0.250928579 Simplifying x = 0.250928579Subproblem 2
x + -0.194375 = -0.056553579 Simplifying x + -0.194375 = -0.056553579 Reorder the terms: -0.194375 + x = -0.056553579 Solving -0.194375 + x = -0.056553579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.194375' to each side of the equation. -0.194375 + 0.194375 + x = -0.056553579 + 0.194375 Combine like terms: -0.194375 + 0.194375 = 0.000000 0.000000 + x = -0.056553579 + 0.194375 x = -0.056553579 + 0.194375 Combine like terms: -0.056553579 + 0.194375 = 0.137821421 x = 0.137821421 Simplifying x = 0.137821421Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.250928579, 0.137821421}
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