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Simplifying 3x4 + -16x2 + -81 = 0 Reorder the terms: -81 + -16x2 + 3x4 = 0 Solving -81 + -16x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -27 + -5.333333333x2 + x4 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -5.333333333x2 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + -5.333333333x2 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -5.333333333x2 + x4 = 0 + 27 -5.333333333x2 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 -5.333333333x2 + x4 = 27 The x term is -5.333333333x2. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333x2 + 7.111111113 + x4 = 27 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x2 + x4 = 27 + 7.111111113 Combine like terms: 27 + 7.111111113 = 34.111111113 7.111111113 + -5.333333333x2 + x4 = 34.111111113 Factor a perfect square on the left side: (x2 + -2.666666667)(x2 + -2.666666667) = 34.111111113 Calculate the square root of the right side: 5.840471823 Break this problem into two subproblems by setting (x2 + -2.666666667) equal to 5.840471823 and -5.840471823.Subproblem 1
x2 + -2.666666667 = 5.840471823 Simplifying x2 + -2.666666667 = 5.840471823 Reorder the terms: -2.666666667 + x2 = 5.840471823 Solving -2.666666667 + x2 = 5.840471823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x2 = 5.840471823 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x2 = 5.840471823 + 2.666666667 x2 = 5.840471823 + 2.666666667 Combine like terms: 5.840471823 + 2.666666667 = 8.50713849 x2 = 8.50713849 Simplifying x2 = 8.50713849 Take the square root of each side: x = {-2.916699931, 2.916699931}Subproblem 2
x2 + -2.666666667 = -5.840471823 Simplifying x2 + -2.666666667 = -5.840471823 Reorder the terms: -2.666666667 + x2 = -5.840471823 Solving -2.666666667 + x2 = -5.840471823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x2 = -5.840471823 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x2 = -5.840471823 + 2.666666667 x2 = -5.840471823 + 2.666666667 Combine like terms: -5.840471823 + 2.666666667 = -3.173805156 x2 = -3.173805156 Simplifying x2 = -3.173805156 Reorder the terms: 3.173805156 + x2 = -3.173805156 + 3.173805156 Combine like terms: -3.173805156 + 3.173805156 = 0.000000000 3.173805156 + 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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