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Simplifying x4 + 4x2 + -177 = 0 Reorder the terms: -177 + 4x2 + x4 = 0 Solving -177 + 4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '177' to each side of the equation. -177 + 4x2 + 177 + x4 = 0 + 177 Reorder the terms: -177 + 177 + 4x2 + x4 = 0 + 177 Combine like terms: -177 + 177 = 0 0 + 4x2 + x4 = 0 + 177 4x2 + x4 = 0 + 177 Combine like terms: 0 + 177 = 177 4x2 + x4 = 177 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 177 + 4 Reorder the terms: 4 + 4x2 + x4 = 177 + 4 Combine like terms: 177 + 4 = 181 4 + 4x2 + x4 = 181 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x2 + 2) equal to 13.453624047 and -13.453624047.Subproblem 1
x2 + 2 = 13.453624047 Simplifying x2 + 2 = 13.453624047 Reorder the terms: 2 + x2 = 13.453624047 Solving 2 + x2 = 13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 13.453624047 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 13.453624047 + -2 x2 = 13.453624047 + -2 Combine like terms: 13.453624047 + -2 = 11.453624047 x2 = 11.453624047 Simplifying x2 = 11.453624047 Take the square root of each side: x = {-3.384320323, 3.384320323}Subproblem 2
x2 + 2 = -13.453624047 Simplifying x2 + 2 = -13.453624047 Reorder the terms: 2 + x2 = -13.453624047 Solving 2 + x2 = -13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -13.453624047 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -13.453624047 + -2 x2 = -13.453624047 + -2 Combine like terms: -13.453624047 + -2 = -15.453624047 x2 = -15.453624047 Simplifying x2 = -15.453624047 Reorder the terms: 15.453624047 + x2 = -15.453624047 + 15.453624047 Combine like terms: -15.453624047 + 15.453624047 = 0.000000000 15.453624047 + 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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