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Simplifying 2x4 + 16x2 = 4 Reorder the terms: 16x2 + 2x4 = 4 Solving 16x2 + 2x4 = 4 Solving for variable 'x'. Reorder the terms: -4 + 16x2 + 2x4 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 16x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 8x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 8x2 + x4)' equal to zero and attempt to solve: Simplifying -2 + 8x2 + x4 = 0 Solving -2 + 8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 8x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + 8x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 8x2 + x4 = 0 + 2 8x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 8x2 + x4 = 2 The x term is 8x2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x2 + 16 + x4 = 2 + 16 Reorder the terms: 16 + 8x2 + x4 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + 8x2 + x4 = 18 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x2 + 4) equal to 4.242640687 and -4.242640687.Subproblem 1
x2 + 4 = 4.242640687 Simplifying x2 + 4 = 4.242640687 Reorder the terms: 4 + x2 = 4.242640687 Solving 4 + x2 = 4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 4.242640687 + -4 x2 = 4.242640687 + -4 Combine like terms: 4.242640687 + -4 = 0.242640687 x2 = 0.242640687 Simplifying x2 = 0.242640687 Take the square root of each side: x = {-0.492585715, 0.492585715}Subproblem 2
x2 + 4 = -4.242640687 Simplifying x2 + 4 = -4.242640687 Reorder the terms: 4 + x2 = -4.242640687 Solving 4 + x2 = -4.242640687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -4.242640687 + -4 x2 = -4.242640687 + -4 Combine like terms: -4.242640687 + -4 = -8.242640687 x2 = -8.242640687 Simplifying x2 = -8.242640687 Reorder the terms: 8.242640687 + x2 = -8.242640687 + 8.242640687 Combine like terms: -8.242640687 + 8.242640687 = 0.000000000 8.242640687 + 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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