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Simplifying 4x4 + 28x2 + 16 = 0 Reorder the terms: 16 + 28x2 + 4x4 = 0 Solving 16 + 28x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 7x2 + x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + 7x2 + x4)' equal to zero and attempt to solve: Simplifying 4 + 7x2 + x4 = 0 Solving 4 + 7x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 7x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + 7x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7x2 + x4 = 0 + -4 7x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 7x2 + x4 = -4 The x term is 7x2. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x2 + 12.25 + x4 = -4 + 12.25 Reorder the terms: 12.25 + 7x2 + x4 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + 7x2 + x4 = 8.25 Factor a perfect square on the left side: (x2 + 3.5)(x2 + 3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x2 + 3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x2 + 3.5 = 2.872281323 Simplifying x2 + 3.5 = 2.872281323 Reorder the terms: 3.5 + x2 = 2.872281323 Solving 3.5 + x2 = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = 2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = 2.872281323 + -3.5 x2 = 2.872281323 + -3.5 Combine like terms: 2.872281323 + -3.5 = -0.627718677 x2 = -0.627718677 Simplifying x2 = -0.627718677 Reorder the terms: 0.627718677 + x2 = -0.627718677 + 0.627718677 Combine like terms: -0.627718677 + 0.627718677 = 0.000000000 0.627718677 + 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 + 3.5 = -2.872281323 Simplifying x2 + 3.5 = -2.872281323 Reorder the terms: 3.5 + x2 = -2.872281323 Solving 3.5 + x2 = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x2 = -2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x2 = -2.872281323 + -3.5 x2 = -2.872281323 + -3.5 Combine like terms: -2.872281323 + -3.5 = -6.372281323 x2 = -6.372281323 Simplifying x2 = -6.372281323 Reorder the terms: 6.372281323 + x2 = -6.372281323 + 6.372281323 Combine like terms: -6.372281323 + 6.372281323 = 0.000000000 6.372281323 + 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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