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Simplifying 0.29x2 + 43.5x + -4239 = 0 Reorder the terms: -4239 + 43.5x + 0.29x2 = 0 Solving -4239 + 43.5x + 0.29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.29 the coefficient of the squared term: Divide each side by '0.29'. -14617.24138 + 150x + x2 = 0 Move the constant term to the right: Add '14617.24138' to each side of the equation. -14617.24138 + 150x + 14617.24138 + x2 = 0 + 14617.24138 Reorder the terms: -14617.24138 + 14617.24138 + 150x + x2 = 0 + 14617.24138 Combine like terms: -14617.24138 + 14617.24138 = 0.00000 0.00000 + 150x + x2 = 0 + 14617.24138 150x + x2 = 0 + 14617.24138 Combine like terms: 0 + 14617.24138 = 14617.24138 150x + x2 = 14617.24138 The x term is 150x. Take half its coefficient (75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. 150x + 5625 + x2 = 14617.24138 + 5625 Reorder the terms: 5625 + 150x + x2 = 14617.24138 + 5625 Combine like terms: 14617.24138 + 5625 = 20242.24138 5625 + 150x + x2 = 20242.24138 Factor a perfect square on the left side: (x + 75)(x + 75) = 20242.24138 Calculate the square root of the right side: 142.275231084 Break this problem into two subproblems by setting (x + 75) equal to 142.275231084 and -142.275231084.Subproblem 1
x + 75 = 142.275231084 Simplifying x + 75 = 142.275231084 Reorder the terms: 75 + x = 142.275231084 Solving 75 + x = 142.275231084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 142.275231084 + -75 Combine like terms: 75 + -75 = 0 0 + x = 142.275231084 + -75 x = 142.275231084 + -75 Combine like terms: 142.275231084 + -75 = 67.275231084 x = 67.275231084 Simplifying x = 67.275231084Subproblem 2
x + 75 = -142.275231084 Simplifying x + 75 = -142.275231084 Reorder the terms: 75 + x = -142.275231084 Solving 75 + x = -142.275231084 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = -142.275231084 + -75 Combine like terms: 75 + -75 = 0 0 + x = -142.275231084 + -75 x = -142.275231084 + -75 Combine like terms: -142.275231084 + -75 = -217.275231084 x = -217.275231084 Simplifying x = -217.275231084Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.275231084, -217.275231084}
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