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Simplifying 2x4 + 4x2 + -10 = 0 Reorder the terms: -10 + 4x2 + 2x4 = 0 Solving -10 + 4x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 2x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 2x2 + x4)' equal to zero and attempt to solve: Simplifying -5 + 2x2 + x4 = 0 Solving -5 + 2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2x2 + 5 + x4 = 0 + 5 Reorder the terms: -5 + 5 + 2x2 + x4 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x2 + x4 = 0 + 5 2x2 + x4 = 0 + 5 Combine like terms: 0 + 5 = 5 2x2 + x4 = 5 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 5 + 1 Reorder the terms: 1 + 2x2 + x4 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2x2 + x4 = 6 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + 1 = 2.449489743 Simplifying x2 + 1 = 2.449489743 Reorder the terms: 1 + x2 = 2.449489743 Solving 1 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 2.449489743 + -1 x2 = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 x2 = 1.449489743 Simplifying x2 = 1.449489743 Take the square root of each side: x = {-1.203947567, 1.203947567}Subproblem 2
x2 + 1 = -2.449489743 Simplifying x2 + 1 = -2.449489743 Reorder the terms: 1 + x2 = -2.449489743 Solving 1 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -2.449489743 + -1 x2 = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 x2 = -3.449489743 Simplifying x2 = -3.449489743 Reorder the terms: 3.449489743 + x2 = -3.449489743 + 3.449489743 Combine like terms: -3.449489743 + 3.449489743 = 0.000000000 3.449489743 + 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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