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Simplifying x4 + 36x2 + 225 = 0 Reorder the terms: 225 + 36x2 + x4 = 0 Solving 225 + 36x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + 36x2 + -225 + x4 = 0 + -225 Reorder the terms: 225 + -225 + 36x2 + x4 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + 36x2 + x4 = 0 + -225 36x2 + x4 = 0 + -225 Combine like terms: 0 + -225 = -225 36x2 + x4 = -225 The x term is 36x2. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x2 + 324 + x4 = -225 + 324 Reorder the terms: 324 + 36x2 + x4 = -225 + 324 Combine like terms: -225 + 324 = 99 324 + 36x2 + x4 = 99 Factor a perfect square on the left side: (x2 + 18)(x2 + 18) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x2 + 18) equal to 9.949874371 and -9.949874371.Subproblem 1
x2 + 18 = 9.949874371 Simplifying x2 + 18 = 9.949874371 Reorder the terms: 18 + x2 = 9.949874371 Solving 18 + x2 = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x2 = 9.949874371 + -18 Combine like terms: 18 + -18 = 0 0 + x2 = 9.949874371 + -18 x2 = 9.949874371 + -18 Combine like terms: 9.949874371 + -18 = -8.050125629 x2 = -8.050125629 Simplifying x2 = -8.050125629 Reorder the terms: 8.050125629 + x2 = -8.050125629 + 8.050125629 Combine like terms: -8.050125629 + 8.050125629 = 0.000000000 8.050125629 + 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 + 18 = -9.949874371 Simplifying x2 + 18 = -9.949874371 Reorder the terms: 18 + x2 = -9.949874371 Solving 18 + x2 = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x2 = -9.949874371 + -18 Combine like terms: 18 + -18 = 0 0 + x2 = -9.949874371 + -18 x2 = -9.949874371 + -18 Combine like terms: -9.949874371 + -18 = -27.949874371 x2 = -27.949874371 Simplifying x2 = -27.949874371 Reorder the terms: 27.949874371 + x2 = -27.949874371 + 27.949874371 Combine like terms: -27.949874371 + 27.949874371 = 0.000000000 27.949874371 + 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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