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Simplifying x4 + -15x2 + -4 = 0 Reorder the terms: -4 + -15x2 + x4 = 0 Solving -4 + -15x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -15x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + -15x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -15x2 + x4 = 0 + 4 -15x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 -15x2 + x4 = 4 The x term is -15x2. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x2 + 56.25 + x4 = 4 + 56.25 Reorder the terms: 56.25 + -15x2 + x4 = 4 + 56.25 Combine like terms: 4 + 56.25 = 60.25 56.25 + -15x2 + x4 = 60.25 Factor a perfect square on the left side: (x2 + -7.5)(x2 + -7.5) = 60.25 Calculate the square root of the right side: 7.762087348 Break this problem into two subproblems by setting (x2 + -7.5) equal to 7.762087348 and -7.762087348.Subproblem 1
x2 + -7.5 = 7.762087348 Simplifying x2 + -7.5 = 7.762087348 Reorder the terms: -7.5 + x2 = 7.762087348 Solving -7.5 + x2 = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = 7.762087348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 7.762087348 + 7.5 x2 = 7.762087348 + 7.5 Combine like terms: 7.762087348 + 7.5 = 15.262087348 x2 = 15.262087348 Simplifying x2 = 15.262087348 Take the square root of each side: x = {-3.906672158, 3.906672158}Subproblem 2
x2 + -7.5 = -7.762087348 Simplifying x2 + -7.5 = -7.762087348 Reorder the terms: -7.5 + x2 = -7.762087348 Solving -7.5 + x2 = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = -7.762087348 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -7.762087348 + 7.5 x2 = -7.762087348 + 7.5 Combine like terms: -7.762087348 + 7.5 = -0.262087348 x2 = -0.262087348 Simplifying x2 = -0.262087348 Reorder the terms: 0.262087348 + x2 = -0.262087348 + 0.262087348 Combine like terms: -0.262087348 + 0.262087348 = 0.000000000 0.262087348 + 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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