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Simplifying 0.05x2 + x = 60 Reorder the terms: x + 0.05x2 = 60 Solving x + 0.05x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + x + 0.05x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + x + 0.05x2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -1200 + 20x + x2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 20x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 20x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 20x + x2 = 0 + 1200 20x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 20x + x2 = 1200 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 20x + 0.25 + x2 = 1200 + 0.25 Reorder the terms: 0.25 + 20x + x2 = 1200 + 0.25 Combine like terms: 1200 + 0.25 = 1200.25 0.25 + 20x + x2 = 1200.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1200.25 Calculate the square root of the right side: 34.644624403 Break this problem into two subproblems by setting (x + 0.5) equal to 34.644624403 and -34.644624403.Subproblem 1
x + 0.5 = 34.644624403 Simplifying x + 0.5 = 34.644624403 Reorder the terms: 0.5 + x = 34.644624403 Solving 0.5 + x = 34.644624403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 34.644624403 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 34.644624403 + -0.5 x = 34.644624403 + -0.5 Combine like terms: 34.644624403 + -0.5 = 34.144624403 x = 34.144624403 Simplifying x = 34.144624403Subproblem 2
x + 0.5 = -34.644624403 Simplifying x + 0.5 = -34.644624403 Reorder the terms: 0.5 + x = -34.644624403 Solving 0.5 + x = -34.644624403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -34.644624403 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -34.644624403 + -0.5 x = -34.644624403 + -0.5 Combine like terms: -34.644624403 + -0.5 = -35.144624403 x = -35.144624403 Simplifying x = -35.144624403Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.144624403, -35.144624403}
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