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Simplifying 2x4 + -1x2 + -216 = 0 Reorder the terms: -216 + -1x2 + 2x4 = 0 Solving -216 + -1x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -108 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + -0.5x2 + 108 + x4 = 0 + 108 Reorder the terms: -108 + 108 + -0.5x2 + x4 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -0.5x2 + x4 = 0 + 108 -0.5x2 + x4 = 0 + 108 Combine like terms: 0 + 108 = 108 -0.5x2 + x4 = 108 The x term is -0.5x2. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x2 + 0.0625 + x4 = 108 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = 108 + 0.0625 Combine like terms: 108 + 0.0625 = 108.0625 0.0625 + -0.5x2 + x4 = 108.0625 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = 108.0625 Calculate the square root of the right side: 10.395311443 Break this problem into two subproblems by setting (x2 + -0.25) equal to 10.395311443 and -10.395311443.Subproblem 1
x2 + -0.25 = 10.395311443 Simplifying x2 + -0.25 = 10.395311443 Reorder the terms: -0.25 + x2 = 10.395311443 Solving -0.25 + x2 = 10.395311443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = 10.395311443 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = 10.395311443 + 0.25 x2 = 10.395311443 + 0.25 Combine like terms: 10.395311443 + 0.25 = 10.645311443 x2 = 10.645311443 Simplifying x2 = 10.645311443 Take the square root of each side: x = {-3.262715348, 3.262715348}Subproblem 2
x2 + -0.25 = -10.395311443 Simplifying x2 + -0.25 = -10.395311443 Reorder the terms: -0.25 + x2 = -10.395311443 Solving -0.25 + x2 = -10.395311443 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = -10.395311443 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = -10.395311443 + 0.25 x2 = -10.395311443 + 0.25 Combine like terms: -10.395311443 + 0.25 = -10.145311443 x2 = -10.145311443 Simplifying x2 = -10.145311443 Reorder the terms: 10.145311443 + x2 = -10.145311443 + 10.145311443 Combine like terms: -10.145311443 + 10.145311443 = 0.000000000 10.145311443 + 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.
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