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Simplifying 16x4 + 56x2 + 4 = 0 Reorder the terms: 4 + 56x2 + 16x4 = 0 Solving 4 + 56x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 14x2 + 4x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 14x2 + 4x4)' equal to zero and attempt to solve: Simplifying 1 + 14x2 + 4x4 = 0 Solving 1 + 14x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 3.5x2 + x4 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.5x2 + -0.25 + x4 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.5x2 + x4 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.5x2 + x4 = 0 + -0.25 3.5x2 + x4 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.5x2 + x4 = -0.25 The x term is 3.5x2. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x2 + 3.0625 + x4 = -0.25 + 3.0625 Reorder the terms: 3.0625 + 3.5x2 + x4 = -0.25 + 3.0625 Combine like terms: -0.25 + 3.0625 = 2.8125 3.0625 + 3.5x2 + x4 = 2.8125 Factor a perfect square on the left side: (x2 + 1.75)(x2 + 1.75) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x2 + 1.75) equal to 1.677050983 and -1.677050983.Subproblem 1
x2 + 1.75 = 1.677050983 Simplifying x2 + 1.75 = 1.677050983 Reorder the terms: 1.75 + x2 = 1.677050983 Solving 1.75 + x2 = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = 1.677050983 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = 1.677050983 + -1.75 x2 = 1.677050983 + -1.75 Combine like terms: 1.677050983 + -1.75 = -0.072949017 x2 = -0.072949017 Simplifying x2 = -0.072949017 Reorder the terms: 0.072949017 + x2 = -0.072949017 + 0.072949017 Combine like terms: -0.072949017 + 0.072949017 = 0.000000000 0.072949017 + 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 + 1.75 = -1.677050983 Simplifying x2 + 1.75 = -1.677050983 Reorder the terms: 1.75 + x2 = -1.677050983 Solving 1.75 + x2 = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = -1.677050983 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = -1.677050983 + -1.75 x2 = -1.677050983 + -1.75 Combine like terms: -1.677050983 + -1.75 = -3.427050983 x2 = -3.427050983 Simplifying x2 = -3.427050983 Reorder the terms: 3.427050983 + x2 = -3.427050983 + 3.427050983 Combine like terms: -3.427050983 + 3.427050983 = 0.000000000 3.427050983 + 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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