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Simplifying 5x4 + 31x2 + -71 = 0 Reorder the terms: -71 + 31x2 + 5x4 = 0 Solving -71 + 31x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14.2 + 6.2x2 + x4 = 0 Move the constant term to the right: Add '14.2' to each side of the equation. -14.2 + 6.2x2 + 14.2 + x4 = 0 + 14.2 Reorder the terms: -14.2 + 14.2 + 6.2x2 + x4 = 0 + 14.2 Combine like terms: -14.2 + 14.2 = 0.0 0.0 + 6.2x2 + x4 = 0 + 14.2 6.2x2 + x4 = 0 + 14.2 Combine like terms: 0 + 14.2 = 14.2 6.2x2 + x4 = 14.2 The x term is 6.2x2. Take half its coefficient (3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. 6.2x2 + 9.61 + x4 = 14.2 + 9.61 Reorder the terms: 9.61 + 6.2x2 + x4 = 14.2 + 9.61 Combine like terms: 14.2 + 9.61 = 23.81 9.61 + 6.2x2 + x4 = 23.81 Factor a perfect square on the left side: (x2 + 3.1)(x2 + 3.1) = 23.81 Calculate the square root of the right side: 4.87954916 Break this problem into two subproblems by setting (x2 + 3.1) equal to 4.87954916 and -4.87954916.Subproblem 1
x2 + 3.1 = 4.87954916 Simplifying x2 + 3.1 = 4.87954916 Reorder the terms: 3.1 + x2 = 4.87954916 Solving 3.1 + x2 = 4.87954916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x2 = 4.87954916 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x2 = 4.87954916 + -3.1 x2 = 4.87954916 + -3.1 Combine like terms: 4.87954916 + -3.1 = 1.77954916 x2 = 1.77954916 Simplifying x2 = 1.77954916 Take the square root of each side: x = {-1.333997436, 1.333997436}Subproblem 2
x2 + 3.1 = -4.87954916 Simplifying x2 + 3.1 = -4.87954916 Reorder the terms: 3.1 + x2 = -4.87954916 Solving 3.1 + x2 = -4.87954916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + x2 = -4.87954916 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + x2 = -4.87954916 + -3.1 x2 = -4.87954916 + -3.1 Combine like terms: -4.87954916 + -3.1 = -7.97954916 x2 = -7.97954916 Simplifying x2 = -7.97954916 Reorder the terms: 7.97954916 + x2 = -7.97954916 + 7.97954916 Combine like terms: -7.97954916 + 7.97954916 = 0.00000000 7.97954916 + 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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