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Simplifying x4 + -20x2 + 60 = 0 Reorder the terms: 60 + -20x2 + x4 = 0 Solving 60 + -20x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -20x2 + -60 + x4 = 0 + -60 Reorder the terms: 60 + -60 + -20x2 + x4 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -20x2 + x4 = 0 + -60 -20x2 + x4 = 0 + -60 Combine like terms: 0 + -60 = -60 -20x2 + x4 = -60 The x term is -20x2. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x2 + 100 + x4 = -60 + 100 Reorder the terms: 100 + -20x2 + x4 = -60 + 100 Combine like terms: -60 + 100 = 40 100 + -20x2 + x4 = 40 Factor a perfect square on the left side: (x2 + -10)(x2 + -10) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x2 + -10) equal to 6.32455532 and -6.32455532.Subproblem 1
x2 + -10 = 6.32455532 Simplifying x2 + -10 = 6.32455532 Reorder the terms: -10 + x2 = 6.32455532 Solving -10 + x2 = 6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = 6.32455532 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 6.32455532 + 10 x2 = 6.32455532 + 10 Combine like terms: 6.32455532 + 10 = 16.32455532 x2 = 16.32455532 Simplifying x2 = 16.32455532 Take the square root of each side: x = {-4.040365741, 4.040365741}Subproblem 2
x2 + -10 = -6.32455532 Simplifying x2 + -10 = -6.32455532 Reorder the terms: -10 + x2 = -6.32455532 Solving -10 + x2 = -6.32455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = -6.32455532 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -6.32455532 + 10 x2 = -6.32455532 + 10 Combine like terms: -6.32455532 + 10 = 3.67544468 x2 = 3.67544468 Simplifying x2 = 3.67544468 Take the square root of each side: x = {-1.917144929, 1.917144929}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.040365741, 4.040365741, -1.917144929, 1.917144929}
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