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Simplifying 4x4 + 20x2 + 4 = 0 Reorder the terms: 4 + 20x2 + 4x4 = 0 Solving 4 + 20x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 5x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 5x2 + x4)' equal to zero and attempt to solve: Simplifying 1 + 5x2 + x4 = 0 Solving 1 + 5x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 5x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x2 + x4 = 0 + -1 5x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 5x2 + x4 = -1 The x term is 5x2. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x2 + 6.25 + x4 = -1 + 6.25 Reorder the terms: 6.25 + 5x2 + x4 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + 5x2 + x4 = 5.25 Factor a perfect square on the left side: (x2 + 2.5)(x2 + 2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x2 + 2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x2 + 2.5 = 2.291287847 Simplifying x2 + 2.5 = 2.291287847 Reorder the terms: 2.5 + x2 = 2.291287847 Solving 2.5 + x2 = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = 2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = 2.291287847 + -2.5 x2 = 2.291287847 + -2.5 Combine like terms: 2.291287847 + -2.5 = -0.208712153 x2 = -0.208712153 Simplifying x2 = -0.208712153 Reorder the terms: 0.208712153 + x2 = -0.208712153 + 0.208712153 Combine like terms: -0.208712153 + 0.208712153 = 0.000000000 0.208712153 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 2.5 = -2.291287847 Simplifying x2 + 2.5 = -2.291287847 Reorder the terms: 2.5 + x2 = -2.291287847 Solving 2.5 + x2 = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x2 = -2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x2 = -2.291287847 + -2.5 x2 = -2.291287847 + -2.5 Combine like terms: -2.291287847 + -2.5 = -4.791287847 x2 = -4.791287847 Simplifying x2 = -4.791287847 Reorder the terms: 4.791287847 + x2 = -4.791287847 + 4.791287847 Combine like terms: -4.791287847 + 4.791287847 = 0.000000000 4.791287847 + 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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