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Simplifying 0 = 4x4 + -483x2 + 121 Reorder the terms: 0 = 121 + -483x2 + 4x4 Solving 0 = 121 + -483x2 + 4x4 Solving for variable 'x'. Combine like terms: 0 + -121 = -121 -121 + 483x2 + -4x4 = 121 + -483x2 + 4x4 + -121 + 483x2 + -4x4 Reorder the terms: -121 + 483x2 + -4x4 = 121 + -121 + -483x2 + 483x2 + 4x4 + -4x4 Combine like terms: 121 + -121 = 0 -121 + 483x2 + -4x4 = 0 + -483x2 + 483x2 + 4x4 + -4x4 -121 + 483x2 + -4x4 = -483x2 + 483x2 + 4x4 + -4x4 Combine like terms: -483x2 + 483x2 = 0 -121 + 483x2 + -4x4 = 0 + 4x4 + -4x4 -121 + 483x2 + -4x4 = 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 -121 + 483x2 + -4x4 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 30.25 + -120.75x2 + x4 = 0 Move the constant term to the right: Add '-30.25' to each side of the equation. 30.25 + -120.75x2 + -30.25 + x4 = 0 + -30.25 Reorder the terms: 30.25 + -30.25 + -120.75x2 + x4 = 0 + -30.25 Combine like terms: 30.25 + -30.25 = 0.00 0.00 + -120.75x2 + x4 = 0 + -30.25 -120.75x2 + x4 = 0 + -30.25 Combine like terms: 0 + -30.25 = -30.25 -120.75x2 + x4 = -30.25 The x term is -120.75x2. Take half its coefficient (-60.375). Square it (3645.140625) and add it to both sides. Add '3645.140625' to each side of the equation. -120.75x2 + 3645.140625 + x4 = -30.25 + 3645.140625 Reorder the terms: 3645.140625 + -120.75x2 + x4 = -30.25 + 3645.140625 Combine like terms: -30.25 + 3645.140625 = 3614.890625 3645.140625 + -120.75x2 + x4 = 3614.890625 Factor a perfect square on the left side: (x2 + -60.375)(x2 + -60.375) = 3614.890625 Calculate the square root of the right side: 60.12396049 Break this problem into two subproblems by setting (x2 + -60.375) equal to 60.12396049 and -60.12396049.Subproblem 1
x2 + -60.375 = 60.12396049 Simplifying x2 + -60.375 = 60.12396049 Reorder the terms: -60.375 + x2 = 60.12396049 Solving -60.375 + x2 = 60.12396049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.375' to each side of the equation. -60.375 + 60.375 + x2 = 60.12396049 + 60.375 Combine like terms: -60.375 + 60.375 = 0.000 0.000 + x2 = 60.12396049 + 60.375 x2 = 60.12396049 + 60.375 Combine like terms: 60.12396049 + 60.375 = 120.49896049 x2 = 120.49896049 Simplifying x2 = 120.49896049 Take the square root of each side: x = {-10.977201852, 10.977201852}Subproblem 2
x2 + -60.375 = -60.12396049 Simplifying x2 + -60.375 = -60.12396049 Reorder the terms: -60.375 + x2 = -60.12396049 Solving -60.375 + x2 = -60.12396049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.375' to each side of the equation. -60.375 + 60.375 + x2 = -60.12396049 + 60.375 Combine like terms: -60.375 + 60.375 = 0.000 0.000 + x2 = -60.12396049 + 60.375 x2 = -60.12396049 + 60.375 Combine like terms: -60.12396049 + 60.375 = 0.25103951 x2 = 0.25103951 Simplifying x2 = 0.25103951 Take the square root of each side: x = {-0.501038432, 0.501038432}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.977201852, 10.977201852, -0.501038432, 0.501038432}
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