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Simplifying x4 + -8x2 + 0.5 = 1 Reorder the terms: 0.5 + -8x2 + x4 = 1 Solving 0.5 + -8x2 + x4 = 1 Solving for variable 'x'. Reorder the terms: 0.5 + -1 + -8x2 + x4 = 1 + -1 Combine like terms: 0.5 + -1 = -0.5 -0.5 + -8x2 + x4 = 1 + -1 Combine like terms: 1 + -1 = 0 -0.5 + -8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -8x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -8x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -8x2 + x4 = 0 + 0.5 -8x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -8x2 + x4 = 0.5 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = 0.5 + 16 Reorder the terms: 16 + -8x2 + x4 = 0.5 + 16 Combine like terms: 0.5 + 16 = 16.5 16 + -8x2 + x4 = 16.5 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (x2 + -4) equal to 4.062019202 and -4.062019202.Subproblem 1
x2 + -4 = 4.062019202 Simplifying x2 + -4 = 4.062019202 Reorder the terms: -4 + x2 = 4.062019202 Solving -4 + x2 = 4.062019202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 4.062019202 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 4.062019202 + 4 x2 = 4.062019202 + 4 Combine like terms: 4.062019202 + 4 = 8.062019202 x2 = 8.062019202 Simplifying x2 = 8.062019202 Take the square root of each side: x = {-2.839369508, 2.839369508}Subproblem 2
x2 + -4 = -4.062019202 Simplifying x2 + -4 = -4.062019202 Reorder the terms: -4 + x2 = -4.062019202 Solving -4 + x2 = -4.062019202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -4.062019202 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -4.062019202 + 4 x2 = -4.062019202 + 4 Combine like terms: -4.062019202 + 4 = -0.062019202 x2 = -0.062019202 Simplifying x2 = -0.062019202 Reorder the terms: 0.062019202 + x2 = -0.062019202 + 0.062019202 Combine like terms: -0.062019202 + 0.062019202 = 0.000000000 0.062019202 + 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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