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Simplifying 2x4 + -1x2 + -56 = 0 Reorder the terms: -56 + -1x2 + 2x4 = 0 Solving -56 + -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'. -28 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -0.5x2 + 28 + x4 = 0 + 28 Reorder the terms: -28 + 28 + -0.5x2 + x4 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -0.5x2 + x4 = 0 + 28 -0.5x2 + x4 = 0 + 28 Combine like terms: 0 + 28 = 28 -0.5x2 + x4 = 28 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 = 28 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = 28 + 0.0625 Combine like terms: 28 + 0.0625 = 28.0625 0.0625 + -0.5x2 + x4 = 28.0625 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = 28.0625 Calculate the square root of the right side: 5.297405025 Break this problem into two subproblems by setting (x2 + -0.25) equal to 5.297405025 and -5.297405025.Subproblem 1
x2 + -0.25 = 5.297405025 Simplifying x2 + -0.25 = 5.297405025 Reorder the terms: -0.25 + x2 = 5.297405025 Solving -0.25 + x2 = 5.297405025 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 = 5.297405025 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = 5.297405025 + 0.25 x2 = 5.297405025 + 0.25 Combine like terms: 5.297405025 + 0.25 = 5.547405025 x2 = 5.547405025 Simplifying x2 = 5.547405025 Take the square root of each side: x = {-2.355292981, 2.355292981}Subproblem 2
x2 + -0.25 = -5.297405025 Simplifying x2 + -0.25 = -5.297405025 Reorder the terms: -0.25 + x2 = -5.297405025 Solving -0.25 + x2 = -5.297405025 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 = -5.297405025 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = -5.297405025 + 0.25 x2 = -5.297405025 + 0.25 Combine like terms: -5.297405025 + 0.25 = -5.047405025 x2 = -5.047405025 Simplifying x2 = -5.047405025 Reorder the terms: 5.047405025 + x2 = -5.047405025 + 5.047405025 Combine like terms: -5.047405025 + 5.047405025 = 0.000000000 5.047405025 + 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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