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Simplifying 4.92x2 + 9.8x + 0 = 3.675 Reorder the terms: 0 + 9.8x + 4.92x2 = 3.675 Remove the zero: 9.8x + 4.92x2 = 3.675 Solving 9.8x + 4.92x2 = 3.675 Solving for variable 'x'. Reorder the terms: -3.675 + 9.8x + 4.92x2 = 3.675 + -3.675 Combine like terms: 3.675 + -3.675 = 0.000 -3.675 + 9.8x + 4.92x2 = 0.000 Begin completing the square. Divide all terms by 4.92 the coefficient of the squared term: Divide each side by '4.92'. -0.7469512195 + 1.991869919x + x2 = 0.0 Move the constant term to the right: Add '0.7469512195' to each side of the equation. -0.7469512195 + 1.991869919x + 0.7469512195 + x2 = 0.0 + 0.7469512195 Reorder the terms: -0.7469512195 + 0.7469512195 + 1.991869919x + x2 = 0.0 + 0.7469512195 Combine like terms: -0.7469512195 + 0.7469512195 = 0.0000000000 0.0000000000 + 1.991869919x + x2 = 0.0 + 0.7469512195 1.991869919x + x2 = 0.0 + 0.7469512195 Combine like terms: 0.0 + 0.7469512195 = 0.7469512195 1.991869919x + x2 = 0.7469512195 The x term is 1.991869919x. Take half its coefficient (0.9959349595). Square it (0.9918864436) and add it to both sides. Add '0.9918864436' to each side of the equation. 1.991869919x + 0.9918864436 + x2 = 0.7469512195 + 0.9918864436 Reorder the terms: 0.9918864436 + 1.991869919x + x2 = 0.7469512195 + 0.9918864436 Combine like terms: 0.7469512195 + 0.9918864436 = 1.7388376631 0.9918864436 + 1.991869919x + x2 = 1.7388376631 Factor a perfect square on the left side: (x + 0.9959349595)(x + 0.9959349595) = 1.7388376631 Calculate the square root of the right side: 1.31864994 Break this problem into two subproblems by setting (x + 0.9959349595) equal to 1.31864994 and -1.31864994.Subproblem 1
x + 0.9959349595 = 1.31864994 Simplifying x + 0.9959349595 = 1.31864994 Reorder the terms: 0.9959349595 + x = 1.31864994 Solving 0.9959349595 + x = 1.31864994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9959349595' to each side of the equation. 0.9959349595 + -0.9959349595 + x = 1.31864994 + -0.9959349595 Combine like terms: 0.9959349595 + -0.9959349595 = 0.0000000000 0.0000000000 + x = 1.31864994 + -0.9959349595 x = 1.31864994 + -0.9959349595 Combine like terms: 1.31864994 + -0.9959349595 = 0.3227149805 x = 0.3227149805 Simplifying x = 0.3227149805Subproblem 2
x + 0.9959349595 = -1.31864994 Simplifying x + 0.9959349595 = -1.31864994 Reorder the terms: 0.9959349595 + x = -1.31864994 Solving 0.9959349595 + x = -1.31864994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9959349595' to each side of the equation. 0.9959349595 + -0.9959349595 + x = -1.31864994 + -0.9959349595 Combine like terms: 0.9959349595 + -0.9959349595 = 0.0000000000 0.0000000000 + x = -1.31864994 + -0.9959349595 x = -1.31864994 + -0.9959349595 Combine like terms: -1.31864994 + -0.9959349595 = -2.3145848995 x = -2.3145848995 Simplifying x = -2.3145848995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3227149805, -2.3145848995}
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