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Simplifying 2x4 + 12x2 = 10 Reorder the terms: 12x2 + 2x4 = 10 Solving 12x2 + 2x4 = 10 Solving for variable 'x'. Reorder the terms: -10 + 12x2 + 2x4 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 12x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 6x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 6x2 + x4)' equal to zero and attempt to solve: Simplifying -5 + 6x2 + x4 = 0 Solving -5 + 6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 6x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + 6x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6x2 + x4 = 0 + 5 6x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 6x2 + x4 = 5 The x term is 6x2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x2 + 9 + x4 = 5 + 9 Reorder the terms: 9 + 6x2 + x4 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6x2 + x4 = 14 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x2 + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
x2 + 3 = 3.741657387 Simplifying x2 + 3 = 3.741657387 Reorder the terms: 3 + x2 = 3.741657387 Solving 3 + x2 = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 3.741657387 + -3 x2 = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 x2 = 0.741657387 Simplifying x2 = 0.741657387 Take the square root of each side: x = {-0.861195325, 0.861195325}Subproblem 2
x2 + 3 = -3.741657387 Simplifying x2 + 3 = -3.741657387 Reorder the terms: 3 + x2 = -3.741657387 Solving 3 + x2 = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -3.741657387 + -3 x2 = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 x2 = -6.741657387 Simplifying x2 = -6.741657387 Reorder the terms: 6.741657387 + x2 = -6.741657387 + 6.741657387 Combine like terms: -6.741657387 + 6.741657387 = 0.000000000 6.741657387 + 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. 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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