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Simplifying x4 + -8x2 = 1440 Reorder the terms: -8x2 + x4 = 1440 Solving -8x2 + x4 = 1440 Solving for variable 'x'. Reorder the terms: -1440 + -8x2 + x4 = 1440 + -1440 Combine like terms: 1440 + -1440 = 0 -1440 + -8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '1440' to each side of the equation. -1440 + -8x2 + 1440 + x4 = 0 + 1440 Reorder the terms: -1440 + 1440 + -8x2 + x4 = 0 + 1440 Combine like terms: -1440 + 1440 = 0 0 + -8x2 + x4 = 0 + 1440 -8x2 + x4 = 0 + 1440 Combine like terms: 0 + 1440 = 1440 -8x2 + x4 = 1440 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 = 1440 + 16 Reorder the terms: 16 + -8x2 + x4 = 1440 + 16 Combine like terms: 1440 + 16 = 1456 16 + -8x2 + x4 = 1456 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 1456 Calculate the square root of the right side: 38.157568057 Break this problem into two subproblems by setting (x2 + -4) equal to 38.157568057 and -38.157568057.Subproblem 1
x2 + -4 = 38.157568057 Simplifying x2 + -4 = 38.157568057 Reorder the terms: -4 + x2 = 38.157568057 Solving -4 + x2 = 38.157568057 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 = 38.157568057 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 38.157568057 + 4 x2 = 38.157568057 + 4 Combine like terms: 38.157568057 + 4 = 42.157568057 x2 = 42.157568057 Simplifying x2 = 42.157568057 Take the square root of each side: x = {-6.492885957, 6.492885957}Subproblem 2
x2 + -4 = -38.157568057 Simplifying x2 + -4 = -38.157568057 Reorder the terms: -4 + x2 = -38.157568057 Solving -4 + x2 = -38.157568057 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 = -38.157568057 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -38.157568057 + 4 x2 = -38.157568057 + 4 Combine like terms: -38.157568057 + 4 = -34.157568057 x2 = -34.157568057 Simplifying x2 = -34.157568057 Reorder the terms: 34.157568057 + x2 = -34.157568057 + 34.157568057 Combine like terms: -34.157568057 + 34.157568057 = 0.000000000 34.157568057 + 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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