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Simplifying x4 + 21x2 + -58 = 0 Reorder the terms: -58 + 21x2 + x4 = 0 Solving -58 + 21x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + 21x2 + 58 + x4 = 0 + 58 Reorder the terms: -58 + 58 + 21x2 + x4 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 21x2 + x4 = 0 + 58 21x2 + x4 = 0 + 58 Combine like terms: 0 + 58 = 58 21x2 + x4 = 58 The x term is 21x2. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x2 + 110.25 + x4 = 58 + 110.25 Reorder the terms: 110.25 + 21x2 + x4 = 58 + 110.25 Combine like terms: 58 + 110.25 = 168.25 110.25 + 21x2 + x4 = 168.25 Factor a perfect square on the left side: (x2 + 10.5)(x2 + 10.5) = 168.25 Calculate the square root of the right side: 12.971121771 Break this problem into two subproblems by setting (x2 + 10.5) equal to 12.971121771 and -12.971121771.Subproblem 1
x2 + 10.5 = 12.971121771 Simplifying x2 + 10.5 = 12.971121771 Reorder the terms: 10.5 + x2 = 12.971121771 Solving 10.5 + x2 = 12.971121771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x2 = 12.971121771 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x2 = 12.971121771 + -10.5 x2 = 12.971121771 + -10.5 Combine like terms: 12.971121771 + -10.5 = 2.471121771 x2 = 2.471121771 Simplifying x2 = 2.471121771 Take the square root of each side: x = {-1.571980207, 1.571980207}Subproblem 2
x2 + 10.5 = -12.971121771 Simplifying x2 + 10.5 = -12.971121771 Reorder the terms: 10.5 + x2 = -12.971121771 Solving 10.5 + x2 = -12.971121771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x2 = -12.971121771 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x2 = -12.971121771 + -10.5 x2 = -12.971121771 + -10.5 Combine like terms: -12.971121771 + -10.5 = -23.471121771 x2 = -23.471121771 Simplifying x2 = -23.471121771 Reorder the terms: 23.471121771 + x2 = -23.471121771 + 23.471121771 Combine like terms: -23.471121771 + 23.471121771 = 0.000000000 23.471121771 + 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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