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Simplifying -1 = -16x2 + 32x Reorder the terms: -1 = 32x + -16x2 Solving -1 = 32x + -16x2 Solving for variable 'x'. Reorder the terms: -1 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -1 + -32x + 16x2 = 0 + -16x2 + 16x2 -1 + -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -1 + -32x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -2x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -2x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -2x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -2x + x2 = 0 + 0.0625 -2x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -2x + x2 = 0.0625 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 = 0.0625 + 1 Reorder the terms: 1 + -2x + x2 = 0.0625 + 1 Combine like terms: 0.0625 + 1 = 1.0625 1 + -2x + x2 = 1.0625 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -1) equal to 1.030776406 and -1.030776406.Subproblem 1
x + -1 = 1.030776406 Simplifying x + -1 = 1.030776406 Reorder the terms: -1 + x = 1.030776406 Solving -1 + x = 1.030776406 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 = 1.030776406 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.030776406 + 1 x = 1.030776406 + 1 Combine like terms: 1.030776406 + 1 = 2.030776406 x = 2.030776406 Simplifying x = 2.030776406Subproblem 2
x + -1 = -1.030776406 Simplifying x + -1 = -1.030776406 Reorder the terms: -1 + x = -1.030776406 Solving -1 + x = -1.030776406 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 = -1.030776406 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.030776406 + 1 x = -1.030776406 + 1 Combine like terms: -1.030776406 + 1 = -0.030776406 x = -0.030776406 Simplifying x = -0.030776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.030776406, -0.030776406}
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