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Simplifying 0 = -16x2 + -2x + 1 Reorder the terms: 0 = 1 + -2x + -16x2 Solving 0 = 1 + -2x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 2x + 16x2 = 1 + -2x + -16x2 + -1 + 2x + 16x2 Reorder the terms: -1 + 2x + 16x2 = 1 + -1 + -2x + 2x + -16x2 + 16x2 Combine like terms: 1 + -1 = 0 -1 + 2x + 16x2 = 0 + -2x + 2x + -16x2 + 16x2 -1 + 2x + 16x2 = -2x + 2x + -16x2 + 16x2 Combine like terms: -2x + 2x = 0 -1 + 2x + 16x2 = 0 + -16x2 + 16x2 -1 + 2x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -1 + 2x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.125x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.125x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.125x + x2 = 0 + 0.0625 0.125x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.125x + x2 = 0.0625 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 0.0625 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 0.0625 + 0.00390625 Combine like terms: 0.0625 + 0.00390625 = 0.06640625 0.00390625 + 0.125x + x2 = 0.06640625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (x + 0.0625) equal to 0.257694102 and -0.257694102.Subproblem 1
x + 0.0625 = 0.257694102 Simplifying x + 0.0625 = 0.257694102 Reorder the terms: 0.0625 + x = 0.257694102 Solving 0.0625 + x = 0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 0.257694102 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.257694102 + -0.0625 x = 0.257694102 + -0.0625 Combine like terms: 0.257694102 + -0.0625 = 0.195194102 x = 0.195194102 Simplifying x = 0.195194102Subproblem 2
x + 0.0625 = -0.257694102 Simplifying x + 0.0625 = -0.257694102 Reorder the terms: 0.0625 + x = -0.257694102 Solving 0.0625 + x = -0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -0.257694102 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -0.257694102 + -0.0625 x = -0.257694102 + -0.0625 Combine like terms: -0.257694102 + -0.0625 = -0.320194102 x = -0.320194102 Simplifying x = -0.320194102Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.195194102, -0.320194102}
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