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Simplifying (x4 + 8x2 + -1) + -1(x2 + -3x2 + -1x4) = 0 Reorder the terms: (-1 + 8x2 + x4) + -1(x2 + -3x2 + -1x4) = 0 Remove parenthesis around (-1 + 8x2 + x4) -1 + 8x2 + x4 + -1(x2 + -3x2 + -1x4) = 0 Combine like terms: x2 + -3x2 = -2x2 -1 + 8x2 + x4 + -1(-2x2 + -1x4) = 0 -1 + 8x2 + x4 + (-2x2 * -1 + -1x4 * -1) = 0 -1 + 8x2 + x4 + (2x2 + 1x4) = 0 Reorder the terms: -1 + 8x2 + 2x2 + x4 + 1x4 = 0 Combine like terms: 8x2 + 2x2 = 10x2 -1 + 10x2 + x4 + 1x4 = 0 Combine like terms: x4 + 1x4 = 2x4 -1 + 10x2 + 2x4 = 0 Solving -1 + 10x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 5x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 5x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 5x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 5x2 + x4 = 0 + 0.5 5x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 5x2 + x4 = 0.5 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = 0.5 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = 0.5 + 6.25 Combine like terms: 0.5 + 6.25 = 6.75 6.25 + 5x2 + x4 = 6.75 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x2 + 2.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x2 + 2.5 = 2.598076211 Simplifying x2 + 2.5 = 2.598076211 Reorder the terms: 2.5 + x2 = 2.598076211 Solving 2.5 + x2 = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 2.598076211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 2.598076211 + -2.5 x2 = 2.598076211 + -2.5 Combine like terms: 2.598076211 + -2.5 = 0.098076211 x2 = 0.098076211 Simplifying x2 = 0.098076211 Take the square root of each side: x = {-0.313171217, 0.313171217}Subproblem 2
x2 + 2.5 = -2.598076211 Simplifying x2 + 2.5 = -2.598076211 Reorder the terms: 2.5 + x2 = -2.598076211 Solving 2.5 + x2 = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -2.598076211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -2.598076211 + -2.5 x2 = -2.598076211 + -2.5 Combine like terms: -2.598076211 + -2.5 = -5.098076211 x2 = -5.098076211 Simplifying x2 = -5.098076211 Reorder the terms: 5.098076211 + x2 = -5.098076211 + 5.098076211 Combine like terms: -5.098076211 + 5.098076211 = 0.000000000 5.098076211 + 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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