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Simplifying x4 + -5x2 + -25 = 0 Reorder the terms: -25 + -5x2 + x4 = 0 Solving -25 + -5x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -5x2 + 25 + x4 = 0 + 25 Reorder the terms: -25 + 25 + -5x2 + x4 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -5x2 + x4 = 0 + 25 -5x2 + x4 = 0 + 25 Combine like terms: 0 + 25 = 25 -5x2 + x4 = 25 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = 25 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = 25 + 6.25 Combine like terms: 25 + 6.25 = 31.25 6.25 + -5x2 + x4 = 31.25 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x2 + -2.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x2 + -2.5 = 5.590169944 Simplifying x2 + -2.5 = 5.590169944 Reorder the terms: -2.5 + x2 = 5.590169944 Solving -2.5 + x2 = 5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 5.590169944 + 2.5 x2 = 5.590169944 + 2.5 Combine like terms: 5.590169944 + 2.5 = 8.090169944 x2 = 8.090169944 Simplifying x2 = 8.090169944 Take the square root of each side: x = {-2.844322405, 2.844322405}Subproblem 2
x2 + -2.5 = -5.590169944 Simplifying x2 + -2.5 = -5.590169944 Reorder the terms: -2.5 + x2 = -5.590169944 Solving -2.5 + x2 = -5.590169944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -5.590169944 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -5.590169944 + 2.5 x2 = -5.590169944 + 2.5 Combine like terms: -5.590169944 + 2.5 = -3.090169944 x2 = -3.090169944 Simplifying x2 = -3.090169944 Reorder the terms: 3.090169944 + x2 = -3.090169944 + 3.090169944 Combine like terms: -3.090169944 + 3.090169944 = 0.000000000 3.090169944 + 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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