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Simplifying x4 + -2x2 + -18 = 0 Reorder the terms: -18 + -2x2 + x4 = 0 Solving -18 + -2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -2x2 + 18 + x4 = 0 + 18 Reorder the terms: -18 + 18 + -2x2 + x4 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2x2 + x4 = 0 + 18 -2x2 + x4 = 0 + 18 Combine like terms: 0 + 18 = 18 -2x2 + x4 = 18 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 18 + 1 Reorder the terms: 1 + -2x2 + x4 = 18 + 1 Combine like terms: 18 + 1 = 19 1 + -2x2 + x4 = 19 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x2 + -1) equal to 4.358898944 and -4.358898944.Subproblem 1
x2 + -1 = 4.358898944 Simplifying x2 + -1 = 4.358898944 Reorder the terms: -1 + x2 = 4.358898944 Solving -1 + x2 = 4.358898944 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 + x2 = 4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 4.358898944 + 1 x2 = 4.358898944 + 1 Combine like terms: 4.358898944 + 1 = 5.358898944 x2 = 5.358898944 Simplifying x2 = 5.358898944 Take the square root of each side: x = {-2.314929576, 2.314929576}Subproblem 2
x2 + -1 = -4.358898944 Simplifying x2 + -1 = -4.358898944 Reorder the terms: -1 + x2 = -4.358898944 Solving -1 + x2 = -4.358898944 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 + x2 = -4.358898944 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -4.358898944 + 1 x2 = -4.358898944 + 1 Combine like terms: -4.358898944 + 1 = -3.358898944 x2 = -3.358898944 Simplifying x2 = -3.358898944 Reorder the terms: 3.358898944 + x2 = -3.358898944 + 3.358898944 Combine like terms: -3.358898944 + 3.358898944 = 0.000000000 3.358898944 + 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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