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Simplifying x4 + x2 + -60 = 0 Reorder the terms: -60 + x2 + x4 = 0 Solving -60 + x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + x2 + 60 + x4 = 0 + 60 Reorder the terms: -60 + 60 + x2 + x4 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + x2 + x4 = 0 + 60 x2 + x4 = 0 + 60 Combine like terms: 0 + 60 = 60 x2 + x4 = 60 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x2 + 0.25 + x4 = 60 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 60 + 0.25 Combine like terms: 60 + 0.25 = 60.25 0.25 + x2 + x4 = 60.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x2 + 0.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x2 + 0.5 = 7.762087348 Simplifying x2 + 0.5 = 7.762087348 Reorder the terms: 0.5 + x2 = 7.762087348 Solving 0.5 + x2 = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 7.762087348 + -0.5 x2 = 7.762087348 + -0.5 Combine like terms: 7.762087348 + -0.5 = 7.262087348 x2 = 7.262087348 Simplifying x2 = 7.262087348 Take the square root of each side: x = {-2.694826033, 2.694826033}Subproblem 2
x2 + 0.5 = -7.762087348 Simplifying x2 + 0.5 = -7.762087348 Reorder the terms: 0.5 + x2 = -7.762087348 Solving 0.5 + x2 = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -7.762087348 + -0.5 x2 = -7.762087348 + -0.5 Combine like terms: -7.762087348 + -0.5 = -8.262087348 x2 = -8.262087348 Simplifying x2 = -8.262087348 Reorder the terms: 8.262087348 + x2 = -8.262087348 + 8.262087348 Combine like terms: -8.262087348 + 8.262087348 = 0.000000000 8.262087348 + 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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