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Simplifying 2X4 + 30X2 + -30 = 0 Reorder the terms: -30 + 30X2 + 2X4 = 0 Solving -30 + 30X2 + 2X4 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 15X2 + X4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 15X2 + X4)' equal to zero and attempt to solve: Simplifying -15 + 15X2 + X4 = 0 Solving -15 + 15X2 + X4 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 15X2 + 15 + X4 = 0 + 15 Reorder the terms: -15 + 15 + 15X2 + X4 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 15X2 + X4 = 0 + 15 15X2 + X4 = 0 + 15 Combine like terms: 0 + 15 = 15 15X2 + X4 = 15 The X term is 15X2. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15X2 + 56.25 + X4 = 15 + 56.25 Reorder the terms: 56.25 + 15X2 + X4 = 15 + 56.25 Combine like terms: 15 + 56.25 = 71.25 56.25 + 15X2 + X4 = 71.25 Factor a perfect square on the left side: (X2 + 7.5)(X2 + 7.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (X2 + 7.5) equal to 8.440971508 and -8.440971508.Subproblem 1
X2 + 7.5 = 8.440971508 Simplifying X2 + 7.5 = 8.440971508 Reorder the terms: 7.5 + X2 = 8.440971508 Solving 7.5 + X2 = 8.440971508 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + X2 = 8.440971508 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X2 = 8.440971508 + -7.5 X2 = 8.440971508 + -7.5 Combine like terms: 8.440971508 + -7.5 = 0.940971508 X2 = 0.940971508 Simplifying X2 = 0.940971508 Take the square root of each side: X = {-0.970036859, 0.970036859}Subproblem 2
X2 + 7.5 = -8.440971508 Simplifying X2 + 7.5 = -8.440971508 Reorder the terms: 7.5 + X2 = -8.440971508 Solving 7.5 + X2 = -8.440971508 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + X2 = -8.440971508 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + X2 = -8.440971508 + -7.5 X2 = -8.440971508 + -7.5 Combine like terms: -8.440971508 + -7.5 = -15.940971508 X2 = -15.940971508 Simplifying X2 = -15.940971508 Reorder the terms: 15.940971508 + X2 = -15.940971508 + 15.940971508 Combine like terms: -15.940971508 + 15.940971508 = 0.000000000 15.940971508 + 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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