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Simplifying 25x4 + 259x2 + 400 = 0 Reorder the terms: 400 + 259x2 + 25x4 = 0 Solving 400 + 259x2 + 25x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 16 + 10.36x2 + x4 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + 10.36x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + 10.36x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 10.36x2 + x4 = 0 + -16 10.36x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 10.36x2 + x4 = -16 The x term is 10.36x2. Take half its coefficient (5.18). Square it (26.8324) and add it to both sides. Add '26.8324' to each side of the equation. 10.36x2 + 26.8324 + x4 = -16 + 26.8324 Reorder the terms: 26.8324 + 10.36x2 + x4 = -16 + 26.8324 Combine like terms: -16 + 26.8324 = 10.8324 26.8324 + 10.36x2 + x4 = 10.8324 Factor a perfect square on the left side: (x2 + 5.18)(x2 + 5.18) = 10.8324 Calculate the square root of the right side: 3.291261156 Break this problem into two subproblems by setting (x2 + 5.18) equal to 3.291261156 and -3.291261156.Subproblem 1
x2 + 5.18 = 3.291261156 Simplifying x2 + 5.18 = 3.291261156 Reorder the terms: 5.18 + x2 = 3.291261156 Solving 5.18 + x2 = 3.291261156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.18' to each side of the equation. 5.18 + -5.18 + x2 = 3.291261156 + -5.18 Combine like terms: 5.18 + -5.18 = 0.00 0.00 + x2 = 3.291261156 + -5.18 x2 = 3.291261156 + -5.18 Combine like terms: 3.291261156 + -5.18 = -1.888738844 x2 = -1.888738844 Simplifying x2 = -1.888738844 Reorder the terms: 1.888738844 + x2 = -1.888738844 + 1.888738844 Combine like terms: -1.888738844 + 1.888738844 = 0.000000000 1.888738844 + 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 + 5.18 = -3.291261156 Simplifying x2 + 5.18 = -3.291261156 Reorder the terms: 5.18 + x2 = -3.291261156 Solving 5.18 + x2 = -3.291261156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.18' to each side of the equation. 5.18 + -5.18 + x2 = -3.291261156 + -5.18 Combine like terms: 5.18 + -5.18 = 0.00 0.00 + x2 = -3.291261156 + -5.18 x2 = -3.291261156 + -5.18 Combine like terms: -3.291261156 + -5.18 = -8.471261156 x2 = -8.471261156 Simplifying x2 = -8.471261156 Reorder the terms: 8.471261156 + x2 = -8.471261156 + 8.471261156 Combine like terms: -8.471261156 + 8.471261156 = 0.000000000 8.471261156 + 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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