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Simplifying 2x4 + 48x2 + 50 = 0 Reorder the terms: 50 + 48x2 + 2x4 = 0 Solving 50 + 48x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 24x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 24x2 + x4)' equal to zero and attempt to solve: Simplifying 25 + 24x2 + x4 = 0 Solving 25 + 24x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 24x2 + -25 + x4 = 0 + -25 Reorder the terms: 25 + -25 + 24x2 + x4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 24x2 + x4 = 0 + -25 24x2 + x4 = 0 + -25 Combine like terms: 0 + -25 = -25 24x2 + x4 = -25 The x term is 24x2. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x2 + 144 + x4 = -25 + 144 Reorder the terms: 144 + 24x2 + x4 = -25 + 144 Combine like terms: -25 + 144 = 119 144 + 24x2 + x4 = 119 Factor a perfect square on the left side: (x2 + 12)(x2 + 12) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (x2 + 12) equal to 10.908712115 and -10.908712115.Subproblem 1
x2 + 12 = 10.908712115 Simplifying x2 + 12 = 10.908712115 Reorder the terms: 12 + x2 = 10.908712115 Solving 12 + x2 = 10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = 10.908712115 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = 10.908712115 + -12 x2 = 10.908712115 + -12 Combine like terms: 10.908712115 + -12 = -1.091287885 x2 = -1.091287885 Simplifying x2 = -1.091287885 Reorder the terms: 1.091287885 + x2 = -1.091287885 + 1.091287885 Combine like terms: -1.091287885 + 1.091287885 = 0.000000000 1.091287885 + 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 + 12 = -10.908712115 Simplifying x2 + 12 = -10.908712115 Reorder the terms: 12 + x2 = -10.908712115 Solving 12 + x2 = -10.908712115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x2 = -10.908712115 + -12 Combine like terms: 12 + -12 = 0 0 + x2 = -10.908712115 + -12 x2 = -10.908712115 + -12 Combine like terms: -10.908712115 + -12 = -22.908712115 x2 = -22.908712115 Simplifying x2 = -22.908712115 Reorder the terms: 22.908712115 + x2 = -22.908712115 + 22.908712115 Combine like terms: -22.908712115 + 22.908712115 = 0.000000000 22.908712115 + 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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