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Simplifying x4 + 2x2 + -47 = 0 Reorder the terms: -47 + 2x2 + x4 = 0 Solving -47 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + 2x2 + 47 + x4 = 0 + 47 Reorder the terms: -47 + 47 + 2x2 + x4 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 2x2 + x4 = 0 + 47 2x2 + x4 = 0 + 47 Combine like terms: 0 + 47 = 47 2x2 + x4 = 47 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 47 + 1 Reorder the terms: 1 + 2x2 + x4 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + 2x2 + x4 = 48 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x2 + 1) equal to 6.92820323 and -6.92820323.Subproblem 1
x2 + 1 = 6.92820323 Simplifying x2 + 1 = 6.92820323 Reorder the terms: 1 + x2 = 6.92820323 Solving 1 + x2 = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 6.92820323 + -1 x2 = 6.92820323 + -1 Combine like terms: 6.92820323 + -1 = 5.92820323 x2 = 5.92820323 Simplifying x2 = 5.92820323 Take the square root of each side: x = {-2.434790182, 2.434790182}Subproblem 2
x2 + 1 = -6.92820323 Simplifying x2 + 1 = -6.92820323 Reorder the terms: 1 + x2 = -6.92820323 Solving 1 + x2 = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -6.92820323 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -6.92820323 + -1 x2 = -6.92820323 + -1 Combine like terms: -6.92820323 + -1 = -7.92820323 x2 = -7.92820323 Simplifying x2 = -7.92820323 Reorder the terms: 7.92820323 + x2 = -7.92820323 + 7.92820323 Combine like terms: -7.92820323 + 7.92820323 = 0.00000000 7.92820323 + x2 = 0.00000000 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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