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Simplifying 20.28 + 32x2 + -50.96x = 0 Reorder the terms: 20.28 + -50.96x + 32x2 = 0 Solving 20.28 + -50.96x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.63375 + -1.5925x + x2 = 0 Move the constant term to the right: Add '-0.63375' to each side of the equation. 0.63375 + -1.5925x + -0.63375 + x2 = 0 + -0.63375 Reorder the terms: 0.63375 + -0.63375 + -1.5925x + x2 = 0 + -0.63375 Combine like terms: 0.63375 + -0.63375 = 0.00000 0.00000 + -1.5925x + x2 = 0 + -0.63375 -1.5925x + x2 = 0 + -0.63375 Combine like terms: 0 + -0.63375 = -0.63375 -1.5925x + x2 = -0.63375 The x term is -1.5925x. Take half its coefficient (-0.79625). Square it (0.6340140625) and add it to both sides. Add '0.6340140625' to each side of the equation. -1.5925x + 0.6340140625 + x2 = -0.63375 + 0.6340140625 Reorder the terms: 0.6340140625 + -1.5925x + x2 = -0.63375 + 0.6340140625 Combine like terms: -0.63375 + 0.6340140625 = 0.0002640625 0.6340140625 + -1.5925x + x2 = 0.0002640625 Factor a perfect square on the left side: (x + -0.79625)(x + -0.79625) = 0.0002640625 Calculate the square root of the right side: 0.01625 Break this problem into two subproblems by setting (x + -0.79625) equal to 0.01625 and -0.01625.Subproblem 1
x + -0.79625 = 0.01625 Simplifying x + -0.79625 = 0.01625 Reorder the terms: -0.79625 + x = 0.01625 Solving -0.79625 + x = 0.01625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.79625' to each side of the equation. -0.79625 + 0.79625 + x = 0.01625 + 0.79625 Combine like terms: -0.79625 + 0.79625 = 0.00000 0.00000 + x = 0.01625 + 0.79625 x = 0.01625 + 0.79625 Combine like terms: 0.01625 + 0.79625 = 0.8125 x = 0.8125 Simplifying x = 0.8125Subproblem 2
x + -0.79625 = -0.01625 Simplifying x + -0.79625 = -0.01625 Reorder the terms: -0.79625 + x = -0.01625 Solving -0.79625 + x = -0.01625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.79625' to each side of the equation. -0.79625 + 0.79625 + x = -0.01625 + 0.79625 Combine like terms: -0.79625 + 0.79625 = 0.00000 0.00000 + x = -0.01625 + 0.79625 x = -0.01625 + 0.79625 Combine like terms: -0.01625 + 0.79625 = 0.78 x = 0.78 Simplifying x = 0.78Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8125, 0.78}
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