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Simplifying x4 + -28x2 + -317 = 0 Reorder the terms: -317 + -28x2 + x4 = 0 Solving -317 + -28x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '317' to each side of the equation. -317 + -28x2 + 317 + x4 = 0 + 317 Reorder the terms: -317 + 317 + -28x2 + x4 = 0 + 317 Combine like terms: -317 + 317 = 0 0 + -28x2 + x4 = 0 + 317 -28x2 + x4 = 0 + 317 Combine like terms: 0 + 317 = 317 -28x2 + x4 = 317 The x term is -28x2. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x2 + 196 + x4 = 317 + 196 Reorder the terms: 196 + -28x2 + x4 = 317 + 196 Combine like terms: 317 + 196 = 513 196 + -28x2 + x4 = 513 Factor a perfect square on the left side: (x2 + -14)(x2 + -14) = 513 Calculate the square root of the right side: 22.649503306 Break this problem into two subproblems by setting (x2 + -14) equal to 22.649503306 and -22.649503306.Subproblem 1
x2 + -14 = 22.649503306 Simplifying x2 + -14 = 22.649503306 Reorder the terms: -14 + x2 = 22.649503306 Solving -14 + x2 = 22.649503306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = 22.649503306 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = 22.649503306 + 14 x2 = 22.649503306 + 14 Combine like terms: 22.649503306 + 14 = 36.649503306 x2 = 36.649503306 Simplifying x2 = 36.649503306 Take the square root of each side: x = {-6.053883324, 6.053883324}Subproblem 2
x2 + -14 = -22.649503306 Simplifying x2 + -14 = -22.649503306 Reorder the terms: -14 + x2 = -22.649503306 Solving -14 + x2 = -22.649503306 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x2 = -22.649503306 + 14 Combine like terms: -14 + 14 = 0 0 + x2 = -22.649503306 + 14 x2 = -22.649503306 + 14 Combine like terms: -22.649503306 + 14 = -8.649503306 x2 = -8.649503306 Simplifying x2 = -8.649503306 Reorder the terms: 8.649503306 + x2 = -8.649503306 + 8.649503306 Combine like terms: -8.649503306 + 8.649503306 = 0.000000000 8.649503306 + 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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