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Simplifying 2x4 + -78x2 = 216 Reorder the terms: -78x2 + 2x4 = 216 Solving -78x2 + 2x4 = 216 Solving for variable 'x'. Reorder the terms: -216 + -78x2 + 2x4 = 216 + -216 Combine like terms: 216 + -216 = 0 -216 + -78x2 + 2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-108 + -39x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-108 + -39x2 + x4)' equal to zero and attempt to solve: Simplifying -108 + -39x2 + x4 = 0 Solving -108 + -39x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -39x2 + 108 + x4 = 0 + 108 Reorder the terms: -108 + 108 + -39x2 + x4 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -39x2 + x4 = 0 + 108 -39x2 + x4 = 0 + 108 Combine like terms: 0 + 108 = 108 -39x2 + x4 = 108 The x term is -39x2. Take half its coefficient (-19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. -39x2 + 380.25 + x4 = 108 + 380.25 Reorder the terms: 380.25 + -39x2 + x4 = 108 + 380.25 Combine like terms: 108 + 380.25 = 488.25 380.25 + -39x2 + x4 = 488.25 Factor a perfect square on the left side: (x2 + -19.5)(x2 + -19.5) = 488.25 Calculate the square root of the right side: 22.096379794 Break this problem into two subproblems by setting (x2 + -19.5) equal to 22.096379794 and -22.096379794.Subproblem 1
x2 + -19.5 = 22.096379794 Simplifying x2 + -19.5 = 22.096379794 Reorder the terms: -19.5 + x2 = 22.096379794 Solving -19.5 + x2 = 22.096379794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x2 = 22.096379794 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x2 = 22.096379794 + 19.5 x2 = 22.096379794 + 19.5 Combine like terms: 22.096379794 + 19.5 = 41.596379794 x2 = 41.596379794 Simplifying x2 = 41.596379794 Take the square root of each side: x = {-6.449525548, 6.449525548}Subproblem 2
x2 + -19.5 = -22.096379794 Simplifying x2 + -19.5 = -22.096379794 Reorder the terms: -19.5 + x2 = -22.096379794 Solving -19.5 + x2 = -22.096379794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x2 = -22.096379794 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x2 = -22.096379794 + 19.5 x2 = -22.096379794 + 19.5 Combine like terms: -22.096379794 + 19.5 = -2.596379794 x2 = -2.596379794 Simplifying x2 = -2.596379794 Reorder the terms: 2.596379794 + x2 = -2.596379794 + 2.596379794 Combine like terms: -2.596379794 + 2.596379794 = 0.000000000 2.596379794 + 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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