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Simplifying 5x4 + 12x2 + -36 = 0 Reorder the terms: -36 + 12x2 + 5x4 = 0 Solving -36 + 12x2 + 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'. -7.2 + 2.4x2 + x4 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 2.4x2 + 7.2 + x4 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 2.4x2 + x4 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 2.4x2 + x4 = 0 + 7.2 2.4x2 + x4 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 2.4x2 + x4 = 7.2 The x term is 2.4x2. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x2 + 1.44 + x4 = 7.2 + 1.44 Reorder the terms: 1.44 + 2.4x2 + x4 = 7.2 + 1.44 Combine like terms: 7.2 + 1.44 = 8.64 1.44 + 2.4x2 + x4 = 8.64 Factor a perfect square on the left side: (x2 + 1.2)(x2 + 1.2) = 8.64 Calculate the square root of the right side: 2.939387691 Break this problem into two subproblems by setting (x2 + 1.2) equal to 2.939387691 and -2.939387691.Subproblem 1
x2 + 1.2 = 2.939387691 Simplifying x2 + 1.2 = 2.939387691 Reorder the terms: 1.2 + x2 = 2.939387691 Solving 1.2 + x2 = 2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x2 = 2.939387691 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x2 = 2.939387691 + -1.2 x2 = 2.939387691 + -1.2 Combine like terms: 2.939387691 + -1.2 = 1.739387691 x2 = 1.739387691 Simplifying x2 = 1.739387691 Take the square root of each side: x = {-1.31885848, 1.31885848}Subproblem 2
x2 + 1.2 = -2.939387691 Simplifying x2 + 1.2 = -2.939387691 Reorder the terms: 1.2 + x2 = -2.939387691 Solving 1.2 + x2 = -2.939387691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x2 = -2.939387691 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x2 = -2.939387691 + -1.2 x2 = -2.939387691 + -1.2 Combine like terms: -2.939387691 + -1.2 = -4.139387691 x2 = -4.139387691 Simplifying x2 = -4.139387691 Reorder the terms: 4.139387691 + x2 = -4.139387691 + 4.139387691 Combine like terms: -4.139387691 + 4.139387691 = 0.000000000 4.139387691 + 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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