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Simplifying 64x2 + -128x + 9 = 0 Reorder the terms: 9 + -128x + 64x2 = 0 Solving 9 + -128x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.140625 + -2x + x2 = 0 Move the constant term to the right: Add '-0.140625' to each side of the equation. 0.140625 + -2x + -0.140625 + x2 = 0 + -0.140625 Reorder the terms: 0.140625 + -0.140625 + -2x + x2 = 0 + -0.140625 Combine like terms: 0.140625 + -0.140625 = 0.000000 0.000000 + -2x + x2 = 0 + -0.140625 -2x + x2 = 0 + -0.140625 Combine like terms: 0 + -0.140625 = -0.140625 -2x + x2 = -0.140625 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.140625 + 1 Reorder the terms: 1 + -2x + x2 = -0.140625 + 1 Combine like terms: -0.140625 + 1 = 0.859375 1 + -2x + x2 = 0.859375 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.859375 Calculate the square root of the right side: 0.927024811 Break this problem into two subproblems by setting (x + -1) equal to 0.927024811 and -0.927024811.Subproblem 1
x + -1 = 0.927024811 Simplifying x + -1 = 0.927024811 Reorder the terms: -1 + x = 0.927024811 Solving -1 + x = 0.927024811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.927024811 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.927024811 + 1 x = 0.927024811 + 1 Combine like terms: 0.927024811 + 1 = 1.927024811 x = 1.927024811 Simplifying x = 1.927024811Subproblem 2
x + -1 = -0.927024811 Simplifying x + -1 = -0.927024811 Reorder the terms: -1 + x = -0.927024811 Solving -1 + x = -0.927024811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.927024811 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.927024811 + 1 x = -0.927024811 + 1 Combine like terms: -0.927024811 + 1 = 0.072975189 x = 0.072975189 Simplifying x = 0.072975189Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.927024811, 0.072975189}
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