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Simplifying 0.04x2 + 0.5x = 80 Reorder the terms: 0.5x + 0.04x2 = 80 Solving 0.5x + 0.04x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 0.5x + 0.04x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 0.5x + 0.04x2 = 0 Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -2000 + 12.5x + x2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 12.5x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 12.5x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 12.5x + x2 = 0 + 2000 12.5x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 12.5x + x2 = 2000 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = 2000 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 2000 + 39.0625 Combine like terms: 2000 + 39.0625 = 2039.0625 39.0625 + 12.5x + x2 = 2039.0625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 2039.0625 Calculate the square root of the right side: 45.15597967 Break this problem into two subproblems by setting (x + 6.25) equal to 45.15597967 and -45.15597967.Subproblem 1
x + 6.25 = 45.15597967 Simplifying x + 6.25 = 45.15597967 Reorder the terms: 6.25 + x = 45.15597967 Solving 6.25 + x = 45.15597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 45.15597967 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 45.15597967 + -6.25 x = 45.15597967 + -6.25 Combine like terms: 45.15597967 + -6.25 = 38.90597967 x = 38.90597967 Simplifying x = 38.90597967Subproblem 2
x + 6.25 = -45.15597967 Simplifying x + 6.25 = -45.15597967 Reorder the terms: 6.25 + x = -45.15597967 Solving 6.25 + x = -45.15597967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -45.15597967 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -45.15597967 + -6.25 x = -45.15597967 + -6.25 Combine like terms: -45.15597967 + -6.25 = -51.40597967 x = -51.40597967 Simplifying x = -51.40597967Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.90597967, -51.40597967}
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