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Simplifying 4x4 + 16x2 + -8 = 0 Reorder the terms: -8 + 16x2 + 4x4 = 0 Solving -8 + 16x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 4x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + 4x2 + x4)' equal to zero and attempt to solve: Simplifying -2 + 4x2 + x4 = 0 Solving -2 + 4x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + 4x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x2 + x4 = 0 + 2 4x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 4x2 + x4 = 2 The x term is 4x2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x2 + 4 + x4 = 2 + 4 Reorder the terms: 4 + 4x2 + x4 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4x2 + x4 = 6 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x2 + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
x2 + 2 = 2.449489743 Simplifying x2 + 2 = 2.449489743 Reorder the terms: 2 + x2 = 2.449489743 Solving 2 + x2 = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 2.449489743 + -2 x2 = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 x2 = 0.449489743 Simplifying x2 = 0.449489743 Take the square root of each side: x = {-0.670439962, 0.670439962}Subproblem 2
x2 + 2 = -2.449489743 Simplifying x2 + 2 = -2.449489743 Reorder the terms: 2 + x2 = -2.449489743 Solving 2 + x2 = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x2 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -2.449489743 + -2 x2 = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 x2 = -4.449489743 Simplifying x2 = -4.449489743 Reorder the terms: 4.449489743 + x2 = -4.449489743 + 4.449489743 Combine like terms: -4.449489743 + 4.449489743 = 0.000000000 4.449489743 + 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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