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Simplifying 3.2x2 + -8.5x + 1.3 = 0 Reorder the terms: 1.3 + -8.5x + 3.2x2 = 0 Solving 1.3 + -8.5x + 3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. 0.40625 + -2.65625x + x2 = 0 Move the constant term to the right: Add '-0.40625' to each side of the equation. 0.40625 + -2.65625x + -0.40625 + x2 = 0 + -0.40625 Reorder the terms: 0.40625 + -0.40625 + -2.65625x + x2 = 0 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + -2.65625x + x2 = 0 + -0.40625 -2.65625x + x2 = 0 + -0.40625 Combine like terms: 0 + -0.40625 = -0.40625 -2.65625x + x2 = -0.40625 The x term is -2.65625x. Take half its coefficient (-1.328125). Square it (1.763916016) and add it to both sides. Add '1.763916016' to each side of the equation. -2.65625x + 1.763916016 + x2 = -0.40625 + 1.763916016 Reorder the terms: 1.763916016 + -2.65625x + x2 = -0.40625 + 1.763916016 Combine like terms: -0.40625 + 1.763916016 = 1.357666016 1.763916016 + -2.65625x + x2 = 1.357666016 Factor a perfect square on the left side: (x + -1.328125)(x + -1.328125) = 1.357666016 Calculate the square root of the right side: 1.165189262 Break this problem into two subproblems by setting (x + -1.328125) equal to 1.165189262 and -1.165189262.Subproblem 1
x + -1.328125 = 1.165189262 Simplifying x + -1.328125 = 1.165189262 Reorder the terms: -1.328125 + x = 1.165189262 Solving -1.328125 + x = 1.165189262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.328125' to each side of the equation. -1.328125 + 1.328125 + x = 1.165189262 + 1.328125 Combine like terms: -1.328125 + 1.328125 = 0.000000 0.000000 + x = 1.165189262 + 1.328125 x = 1.165189262 + 1.328125 Combine like terms: 1.165189262 + 1.328125 = 2.493314262 x = 2.493314262 Simplifying x = 2.493314262Subproblem 2
x + -1.328125 = -1.165189262 Simplifying x + -1.328125 = -1.165189262 Reorder the terms: -1.328125 + x = -1.165189262 Solving -1.328125 + x = -1.165189262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.328125' to each side of the equation. -1.328125 + 1.328125 + x = -1.165189262 + 1.328125 Combine like terms: -1.328125 + 1.328125 = 0.000000 0.000000 + x = -1.165189262 + 1.328125 x = -1.165189262 + 1.328125 Combine like terms: -1.165189262 + 1.328125 = 0.162935738 x = 0.162935738 Simplifying x = 0.162935738Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.493314262, 0.162935738}
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