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Simplifying x4 + -2x2 + -20 = 0 Reorder the terms: -20 + -2x2 + x4 = 0 Solving -20 + -2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -2x2 + 20 + x4 = 0 + 20 Reorder the terms: -20 + 20 + -2x2 + x4 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -2x2 + x4 = 0 + 20 -2x2 + x4 = 0 + 20 Combine like terms: 0 + 20 = 20 -2x2 + x4 = 20 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 = 20 + 1 Reorder the terms: 1 + -2x2 + x4 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + -2x2 + x4 = 21 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x2 + -1) equal to 4.582575695 and -4.582575695.Subproblem 1
x2 + -1 = 4.582575695 Simplifying x2 + -1 = 4.582575695 Reorder the terms: -1 + x2 = 4.582575695 Solving -1 + x2 = 4.582575695 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 = 4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 4.582575695 + 1 x2 = 4.582575695 + 1 Combine like terms: 4.582575695 + 1 = 5.582575695 x2 = 5.582575695 Simplifying x2 = 5.582575695 Take the square root of each side: x = {-2.362747489, 2.362747489}Subproblem 2
x2 + -1 = -4.582575695 Simplifying x2 + -1 = -4.582575695 Reorder the terms: -1 + x2 = -4.582575695 Solving -1 + x2 = -4.582575695 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 = -4.582575695 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -4.582575695 + 1 x2 = -4.582575695 + 1 Combine like terms: -4.582575695 + 1 = -3.582575695 x2 = -3.582575695 Simplifying x2 = -3.582575695 Reorder the terms: 3.582575695 + x2 = -3.582575695 + 3.582575695 Combine like terms: -3.582575695 + 3.582575695 = 0.000000000 3.582575695 + 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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