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Simplifying x4 + 21x2 + 100 = 0 Reorder the terms: 100 + 21x2 + x4 = 0 Solving 100 + 21x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 21x2 + -100 + x4 = 0 + -100 Reorder the terms: 100 + -100 + 21x2 + x4 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 21x2 + x4 = 0 + -100 21x2 + x4 = 0 + -100 Combine like terms: 0 + -100 = -100 21x2 + x4 = -100 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 = -100 + 110.25 Reorder the terms: 110.25 + 21x2 + x4 = -100 + 110.25 Combine like terms: -100 + 110.25 = 10.25 110.25 + 21x2 + x4 = 10.25 Factor a perfect square on the left side: (x2 + 10.5)(x2 + 10.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x2 + 10.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x2 + 10.5 = 3.201562119 Simplifying x2 + 10.5 = 3.201562119 Reorder the terms: 10.5 + x2 = 3.201562119 Solving 10.5 + x2 = 3.201562119 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 = 3.201562119 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x2 = 3.201562119 + -10.5 x2 = 3.201562119 + -10.5 Combine like terms: 3.201562119 + -10.5 = -7.298437881 x2 = -7.298437881 Simplifying x2 = -7.298437881 Reorder the terms: 7.298437881 + x2 = -7.298437881 + 7.298437881 Combine like terms: -7.298437881 + 7.298437881 = 0.000000000 7.298437881 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 10.5 = -3.201562119 Simplifying x2 + 10.5 = -3.201562119 Reorder the terms: 10.5 + x2 = -3.201562119 Solving 10.5 + x2 = -3.201562119 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 = -3.201562119 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x2 = -3.201562119 + -10.5 x2 = -3.201562119 + -10.5 Combine like terms: -3.201562119 + -10.5 = -13.701562119 x2 = -13.701562119 Simplifying x2 = -13.701562119 Reorder the terms: 13.701562119 + x2 = -13.701562119 + 13.701562119 Combine like terms: -13.701562119 + 13.701562119 = 0.000000000 13.701562119 + 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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