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Simplifying x4 + 35x2 + 81 = 0 Reorder the terms: 81 + 35x2 + x4 = 0 Solving 81 + 35x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + 35x2 + -81 + x4 = 0 + -81 Reorder the terms: 81 + -81 + 35x2 + x4 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 35x2 + x4 = 0 + -81 35x2 + x4 = 0 + -81 Combine like terms: 0 + -81 = -81 35x2 + x4 = -81 The x term is 35x2. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x2 + 306.25 + x4 = -81 + 306.25 Reorder the terms: 306.25 + 35x2 + x4 = -81 + 306.25 Combine like terms: -81 + 306.25 = 225.25 306.25 + 35x2 + x4 = 225.25 Factor a perfect square on the left side: (x2 + 17.5)(x2 + 17.5) = 225.25 Calculate the square root of the right side: 15.00833102 Break this problem into two subproblems by setting (x2 + 17.5) equal to 15.00833102 and -15.00833102.Subproblem 1
x2 + 17.5 = 15.00833102 Simplifying x2 + 17.5 = 15.00833102 Reorder the terms: 17.5 + x2 = 15.00833102 Solving 17.5 + x2 = 15.00833102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x2 = 15.00833102 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x2 = 15.00833102 + -17.5 x2 = 15.00833102 + -17.5 Combine like terms: 15.00833102 + -17.5 = -2.49166898 x2 = -2.49166898 Simplifying x2 = -2.49166898 Reorder the terms: 2.49166898 + x2 = -2.49166898 + 2.49166898 Combine like terms: -2.49166898 + 2.49166898 = 0.00000000 2.49166898 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 17.5 = -15.00833102 Simplifying x2 + 17.5 = -15.00833102 Reorder the terms: 17.5 + x2 = -15.00833102 Solving 17.5 + x2 = -15.00833102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x2 = -15.00833102 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x2 = -15.00833102 + -17.5 x2 = -15.00833102 + -17.5 Combine like terms: -15.00833102 + -17.5 = -32.50833102 x2 = -32.50833102 Simplifying x2 = -32.50833102 Reorder the terms: 32.50833102 + x2 = -32.50833102 + 32.50833102 Combine like terms: -32.50833102 + 32.50833102 = 0.00000000 32.50833102 + 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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