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Simplifying x4 + -2x2 + -54 = 0 Reorder the terms: -54 + -2x2 + x4 = 0 Solving -54 + -2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -2x2 + 54 + x4 = 0 + 54 Reorder the terms: -54 + 54 + -2x2 + x4 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -2x2 + x4 = 0 + 54 -2x2 + x4 = 0 + 54 Combine like terms: 0 + 54 = 54 -2x2 + x4 = 54 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 = 54 + 1 Reorder the terms: 1 + -2x2 + x4 = 54 + 1 Combine like terms: 54 + 1 = 55 1 + -2x2 + x4 = 55 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x2 + -1) equal to 7.416198487 and -7.416198487.Subproblem 1
x2 + -1 = 7.416198487 Simplifying x2 + -1 = 7.416198487 Reorder the terms: -1 + x2 = 7.416198487 Solving -1 + x2 = 7.416198487 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 = 7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 7.416198487 + 1 x2 = 7.416198487 + 1 Combine like terms: 7.416198487 + 1 = 8.416198487 x2 = 8.416198487 Simplifying x2 = 8.416198487 Take the square root of each side: x = {-2.901068508, 2.901068508}Subproblem 2
x2 + -1 = -7.416198487 Simplifying x2 + -1 = -7.416198487 Reorder the terms: -1 + x2 = -7.416198487 Solving -1 + x2 = -7.416198487 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 = -7.416198487 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -7.416198487 + 1 x2 = -7.416198487 + 1 Combine like terms: -7.416198487 + 1 = -6.416198487 x2 = -6.416198487 Simplifying x2 = -6.416198487 Reorder the terms: 6.416198487 + x2 = -6.416198487 + 6.416198487 Combine like terms: -6.416198487 + 6.416198487 = 0.000000000 6.416198487 + 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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