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Simplifying 3.5x + x2 = 81 Solving 3.5x + x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + 3.5x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 3.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 3.5x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 3.5x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 3.5x + x2 = 0 + 81 3.5x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 3.5x + x2 = 81 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 81 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 81 + 3.0625 Combine like terms: 81 + 3.0625 = 84.0625 3.0625 + 3.5x + x2 = 84.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 84.0625 Calculate the square root of the right side: 9.16856041 Break this problem into two subproblems by setting (x + 1.75) equal to 9.16856041 and -9.16856041.Subproblem 1
x + 1.75 = 9.16856041 Simplifying x + 1.75 = 9.16856041 Reorder the terms: 1.75 + x = 9.16856041 Solving 1.75 + x = 9.16856041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 9.16856041 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 9.16856041 + -1.75 x = 9.16856041 + -1.75 Combine like terms: 9.16856041 + -1.75 = 7.41856041 x = 7.41856041 Simplifying x = 7.41856041Subproblem 2
x + 1.75 = -9.16856041 Simplifying x + 1.75 = -9.16856041 Reorder the terms: 1.75 + x = -9.16856041 Solving 1.75 + x = -9.16856041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -9.16856041 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -9.16856041 + -1.75 x = -9.16856041 + -1.75 Combine like terms: -9.16856041 + -1.75 = -10.91856041 x = -10.91856041 Simplifying x = -10.91856041Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.41856041, -10.91856041}
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