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Simplifying 20x2 + 10x + -1 + -20 = 0 Reorder the terms: -1 + -20 + 10x + 20x2 = 0 Combine like terms: -1 + -20 = -21 -21 + 10x + 20x2 = 0 Solving -21 + 10x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1.05 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.05' to each side of the equation. -1.05 + 0.5x + 1.05 + x2 = 0 + 1.05 Reorder the terms: -1.05 + 1.05 + 0.5x + x2 = 0 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + 0.5x + x2 = 0 + 1.05 0.5x + x2 = 0 + 1.05 Combine like terms: 0 + 1.05 = 1.05 0.5x + x2 = 1.05 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.05 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.05 + 0.0625 Combine like terms: 1.05 + 0.0625 = 1.1125 0.0625 + 0.5x + x2 = 1.1125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.1125 Calculate the square root of the right side: 1.054751155 Break this problem into two subproblems by setting (x + 0.25) equal to 1.054751155 and -1.054751155.Subproblem 1
x + 0.25 = 1.054751155 Simplifying x + 0.25 = 1.054751155 Reorder the terms: 0.25 + x = 1.054751155 Solving 0.25 + x = 1.054751155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.054751155 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.054751155 + -0.25 x = 1.054751155 + -0.25 Combine like terms: 1.054751155 + -0.25 = 0.804751155 x = 0.804751155 Simplifying x = 0.804751155Subproblem 2
x + 0.25 = -1.054751155 Simplifying x + 0.25 = -1.054751155 Reorder the terms: 0.25 + x = -1.054751155 Solving 0.25 + x = -1.054751155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.054751155 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.054751155 + -0.25 x = -1.054751155 + -0.25 Combine like terms: -1.054751155 + -0.25 = -1.304751155 x = -1.304751155 Simplifying x = -1.304751155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.804751155, -1.304751155}
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