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Simplifying 4x4 + 21x2 + -100 = 0 Reorder the terms: -100 + 21x2 + 4x4 = 0 Solving -100 + 21x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -25 + 5.25x2 + x4 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 5.25x2 + 25 + x4 = 0 + 25 Reorder the terms: -25 + 25 + 5.25x2 + x4 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 5.25x2 + x4 = 0 + 25 5.25x2 + x4 = 0 + 25 Combine like terms: 0 + 25 = 25 5.25x2 + x4 = 25 The x term is 5.25x2. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x2 + 6.890625 + x4 = 25 + 6.890625 Reorder the terms: 6.890625 + 5.25x2 + x4 = 25 + 6.890625 Combine like terms: 25 + 6.890625 = 31.890625 6.890625 + 5.25x2 + x4 = 31.890625 Factor a perfect square on the left side: (x2 + 2.625)(x2 + 2.625) = 31.890625 Calculate the square root of the right side: 5.647178499 Break this problem into two subproblems by setting (x2 + 2.625) equal to 5.647178499 and -5.647178499.Subproblem 1
x2 + 2.625 = 5.647178499 Simplifying x2 + 2.625 = 5.647178499 Reorder the terms: 2.625 + x2 = 5.647178499 Solving 2.625 + x2 = 5.647178499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x2 = 5.647178499 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x2 = 5.647178499 + -2.625 x2 = 5.647178499 + -2.625 Combine like terms: 5.647178499 + -2.625 = 3.022178499 x2 = 3.022178499 Simplifying x2 = 3.022178499 Take the square root of each side: x = {-1.738441399, 1.738441399}Subproblem 2
x2 + 2.625 = -5.647178499 Simplifying x2 + 2.625 = -5.647178499 Reorder the terms: 2.625 + x2 = -5.647178499 Solving 2.625 + x2 = -5.647178499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x2 = -5.647178499 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x2 = -5.647178499 + -2.625 x2 = -5.647178499 + -2.625 Combine like terms: -5.647178499 + -2.625 = -8.272178499 x2 = -8.272178499 Simplifying x2 = -8.272178499 Reorder the terms: 8.272178499 + x2 = -8.272178499 + 8.272178499 Combine like terms: -8.272178499 + 8.272178499 = 0.000000000 8.272178499 + 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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