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Simplifying 5x4 + 18x2 + -27 = 0 Reorder the terms: -27 + 18x2 + 5x4 = 0 Solving -27 + 18x2 + 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'. -5.4 + 3.6x2 + x4 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 3.6x2 + 5.4 + x4 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 3.6x2 + x4 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 3.6x2 + x4 = 0 + 5.4 3.6x2 + x4 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 3.6x2 + x4 = 5.4 The x term is 3.6x2. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x2 + 3.24 + x4 = 5.4 + 3.24 Reorder the terms: 3.24 + 3.6x2 + x4 = 5.4 + 3.24 Combine like terms: 5.4 + 3.24 = 8.64 3.24 + 3.6x2 + x4 = 8.64 Factor a perfect square on the left side: (x2 + 1.8)(x2 + 1.8) = 8.64 Calculate the square root of the right side: 2.939387691 Break this problem into two subproblems by setting (x2 + 1.8) equal to 2.939387691 and -2.939387691.Subproblem 1
x2 + 1.8 = 2.939387691 Simplifying x2 + 1.8 = 2.939387691 Reorder the terms: 1.8 + x2 = 2.939387691 Solving 1.8 + x2 = 2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x2 = 2.939387691 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x2 = 2.939387691 + -1.8 x2 = 2.939387691 + -1.8 Combine like terms: 2.939387691 + -1.8 = 1.139387691 x2 = 1.139387691 Simplifying x2 = 1.139387691 Take the square root of each side: x = {-1.067421047, 1.067421047}Subproblem 2
x2 + 1.8 = -2.939387691 Simplifying x2 + 1.8 = -2.939387691 Reorder the terms: 1.8 + x2 = -2.939387691 Solving 1.8 + x2 = -2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x2 = -2.939387691 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x2 = -2.939387691 + -1.8 x2 = -2.939387691 + -1.8 Combine like terms: -2.939387691 + -1.8 = -4.739387691 x2 = -4.739387691 Simplifying x2 = -4.739387691 Reorder the terms: 4.739387691 + x2 = -4.739387691 + 4.739387691 Combine like terms: -4.739387691 + 4.739387691 = 0.000000000 4.739387691 + 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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