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Simplifying 2x4 + 18x2 + -243 = 0 Reorder the terms: -243 + 18x2 + 2x4 = 0 Solving -243 + 18x2 + 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'. -121.5 + 9x2 + x4 = 0 Move the constant term to the right: Add '121.5' to each side of the equation. -121.5 + 9x2 + 121.5 + x4 = 0 + 121.5 Reorder the terms: -121.5 + 121.5 + 9x2 + x4 = 0 + 121.5 Combine like terms: -121.5 + 121.5 = 0.0 0.0 + 9x2 + x4 = 0 + 121.5 9x2 + x4 = 0 + 121.5 Combine like terms: 0 + 121.5 = 121.5 9x2 + x4 = 121.5 The x term is 9x2. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x2 + 20.25 + x4 = 121.5 + 20.25 Reorder the terms: 20.25 + 9x2 + x4 = 121.5 + 20.25 Combine like terms: 121.5 + 20.25 = 141.75 20.25 + 9x2 + x4 = 141.75 Factor a perfect square on the left side: (x2 + 4.5)(x2 + 4.5) = 141.75 Calculate the square root of the right side: 11.9058809 Break this problem into two subproblems by setting (x2 + 4.5) equal to 11.9058809 and -11.9058809.Subproblem 1
x2 + 4.5 = 11.9058809 Simplifying x2 + 4.5 = 11.9058809 Reorder the terms: 4.5 + x2 = 11.9058809 Solving 4.5 + x2 = 11.9058809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = 11.9058809 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = 11.9058809 + -4.5 x2 = 11.9058809 + -4.5 Combine like terms: 11.9058809 + -4.5 = 7.4058809 x2 = 7.4058809 Simplifying x2 = 7.4058809 Take the square root of each side: x = {-2.721374818, 2.721374818}Subproblem 2
x2 + 4.5 = -11.9058809 Simplifying x2 + 4.5 = -11.9058809 Reorder the terms: 4.5 + x2 = -11.9058809 Solving 4.5 + x2 = -11.9058809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x2 = -11.9058809 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x2 = -11.9058809 + -4.5 x2 = -11.9058809 + -4.5 Combine like terms: -11.9058809 + -4.5 = -16.4058809 x2 = -16.4058809 Simplifying x2 = -16.4058809 Reorder the terms: 16.4058809 + x2 = -16.4058809 + 16.4058809 Combine like terms: -16.4058809 + 16.4058809 = 0.0000000 16.4058809 + x2 = 0.0000000 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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