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Simplifying 16x4 + -8x2 = 1 Reorder the terms: -8x2 + 16x4 = 1 Solving -8x2 + 16x4 = 1 Solving for variable 'x'. Reorder the terms: -1 + -8x2 + 16x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -8x2 + 16x4 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.5x2 + 0.0625 + x4 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.5x2 + x4 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.5x2 + x4 = 0 + 0.0625 -0.5x2 + x4 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.5x2 + x4 = 0.0625 The x term is -0.5x2. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x2 + 0.0625 + x4 = 0.0625 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = 0.0625 + 0.0625 Combine like terms: 0.0625 + 0.0625 = 0.125 0.0625 + -0.5x2 + x4 = 0.125 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x2 + -0.25) equal to 0.353553391 and -0.353553391.Subproblem 1
x2 + -0.25 = 0.353553391 Simplifying x2 + -0.25 = 0.353553391 Reorder the terms: -0.25 + x2 = 0.353553391 Solving -0.25 + x2 = 0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = 0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = 0.353553391 + 0.25 x2 = 0.353553391 + 0.25 Combine like terms: 0.353553391 + 0.25 = 0.603553391 x2 = 0.603553391 Simplifying x2 = 0.603553391 Take the square root of each side: x = {-0.776886987, 0.776886987}Subproblem 2
x2 + -0.25 = -0.353553391 Simplifying x2 + -0.25 = -0.353553391 Reorder the terms: -0.25 + x2 = -0.353553391 Solving -0.25 + x2 = -0.353553391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = -0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = -0.353553391 + 0.25 x2 = -0.353553391 + 0.25 Combine like terms: -0.353553391 + 0.25 = -0.103553391 x2 = -0.103553391 Simplifying x2 = -0.103553391 Reorder the terms: 0.103553391 + x2 = -0.103553391 + 0.103553391 Combine like terms: -0.103553391 + 0.103553391 = 0.000000000 0.103553391 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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