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Simplifying 25x2 + x4 + 16 = 0 Reorder the terms: 16 + 25x2 + x4 = 0 Solving 16 + 25x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 25x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + 25x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 25x2 + x4 = 0 + -16 25x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 25x2 + x4 = -16 The x term is 25x2. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x2 + 156.25 + x4 = -16 + 156.25 Reorder the terms: 156.25 + 25x2 + x4 = -16 + 156.25 Combine like terms: -16 + 156.25 = 140.25 156.25 + 25x2 + x4 = 140.25 Factor a perfect square on the left side: (x2 + 12.5)(x2 + 12.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x2 + 12.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x2 + 12.5 = 11.842719282 Simplifying x2 + 12.5 = 11.842719282 Reorder the terms: 12.5 + x2 = 11.842719282 Solving 12.5 + x2 = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x2 = 11.842719282 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x2 = 11.842719282 + -12.5 x2 = 11.842719282 + -12.5 Combine like terms: 11.842719282 + -12.5 = -0.657280718 x2 = -0.657280718 Simplifying x2 = -0.657280718 Reorder the terms: 0.657280718 + x2 = -0.657280718 + 0.657280718 Combine like terms: -0.657280718 + 0.657280718 = 0.000000000 0.657280718 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 12.5 = -11.842719282 Simplifying x2 + 12.5 = -11.842719282 Reorder the terms: 12.5 + x2 = -11.842719282 Solving 12.5 + x2 = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x2 = -11.842719282 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x2 = -11.842719282 + -12.5 x2 = -11.842719282 + -12.5 Combine like terms: -11.842719282 + -12.5 = -24.342719282 x2 = -24.342719282 Simplifying x2 = -24.342719282 Reorder the terms: 24.342719282 + x2 = -24.342719282 + 24.342719282 Combine like terms: -24.342719282 + 24.342719282 = 0.000000000 24.342719282 + 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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