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Simplifying 27x4 + -208x2 + 320 = 0 Reorder the terms: 320 + -208x2 + 27x4 = 0 Solving 320 + -208x2 + 27x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 11.85185185 + -7.703703704x2 + x4 = 0 Move the constant term to the right: Add '-11.85185185' to each side of the equation. 11.85185185 + -7.703703704x2 + -11.85185185 + x4 = 0 + -11.85185185 Reorder the terms: 11.85185185 + -11.85185185 + -7.703703704x2 + x4 = 0 + -11.85185185 Combine like terms: 11.85185185 + -11.85185185 = 0.00000000 0.00000000 + -7.703703704x2 + x4 = 0 + -11.85185185 -7.703703704x2 + x4 = 0 + -11.85185185 Combine like terms: 0 + -11.85185185 = -11.85185185 -7.703703704x2 + x4 = -11.85185185 The x term is -7.703703704x2. Take half its coefficient (-3.851851852). Square it (14.83676269) and add it to both sides. Add '14.83676269' to each side of the equation. -7.703703704x2 + 14.83676269 + x4 = -11.85185185 + 14.83676269 Reorder the terms: 14.83676269 + -7.703703704x2 + x4 = -11.85185185 + 14.83676269 Combine like terms: -11.85185185 + 14.83676269 = 2.98491084 14.83676269 + -7.703703704x2 + x4 = 2.98491084 Factor a perfect square on the left side: (x2 + -3.851851852)(x2 + -3.851851852) = 2.98491084 Calculate the square root of the right side: 1.727689451 Break this problem into two subproblems by setting (x2 + -3.851851852) equal to 1.727689451 and -1.727689451.Subproblem 1
x2 + -3.851851852 = 1.727689451 Simplifying x2 + -3.851851852 = 1.727689451 Reorder the terms: -3.851851852 + x2 = 1.727689451 Solving -3.851851852 + x2 = 1.727689451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.851851852' to each side of the equation. -3.851851852 + 3.851851852 + x2 = 1.727689451 + 3.851851852 Combine like terms: -3.851851852 + 3.851851852 = 0.000000000 0.000000000 + x2 = 1.727689451 + 3.851851852 x2 = 1.727689451 + 3.851851852 Combine like terms: 1.727689451 + 3.851851852 = 5.579541303 x2 = 5.579541303 Simplifying x2 = 5.579541303 Take the square root of each side: x = {-2.362105269, 2.362105269}Subproblem 2
x2 + -3.851851852 = -1.727689451 Simplifying x2 + -3.851851852 = -1.727689451 Reorder the terms: -3.851851852 + x2 = -1.727689451 Solving -3.851851852 + x2 = -1.727689451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.851851852' to each side of the equation. -3.851851852 + 3.851851852 + x2 = -1.727689451 + 3.851851852 Combine like terms: -3.851851852 + 3.851851852 = 0.000000000 0.000000000 + x2 = -1.727689451 + 3.851851852 x2 = -1.727689451 + 3.851851852 Combine like terms: -1.727689451 + 3.851851852 = 2.124162401 x2 = 2.124162401 Simplifying x2 = 2.124162401 Take the square root of each side: x = {-1.457450651, 1.457450651}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.362105269, 2.362105269, -1.457450651, 1.457450651}
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