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Simplifying x4 + -18x2 + 31 = 0 Reorder the terms: 31 + -18x2 + x4 = 0 Solving 31 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + -18x2 + -31 + x4 = 0 + -31 Reorder the terms: 31 + -31 + -18x2 + x4 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -18x2 + x4 = 0 + -31 -18x2 + x4 = 0 + -31 Combine like terms: 0 + -31 = -31 -18x2 + x4 = -31 The x term is -18x2. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x2 + 81 + x4 = -31 + 81 Reorder the terms: 81 + -18x2 + x4 = -31 + 81 Combine like terms: -31 + 81 = 50 81 + -18x2 + x4 = 50 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x2 + -9) equal to 7.071067812 and -7.071067812.Subproblem 1
x2 + -9 = 7.071067812 Simplifying x2 + -9 = 7.071067812 Reorder the terms: -9 + x2 = 7.071067812 Solving -9 + x2 = 7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = 7.071067812 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 7.071067812 + 9 x2 = 7.071067812 + 9 Combine like terms: 7.071067812 + 9 = 16.071067812 x2 = 16.071067812 Simplifying x2 = 16.071067812 Take the square root of each side: x = {-4.008873634, 4.008873634}Subproblem 2
x2 + -9 = -7.071067812 Simplifying x2 + -9 = -7.071067812 Reorder the terms: -9 + x2 = -7.071067812 Solving -9 + x2 = -7.071067812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x2 = -7.071067812 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -7.071067812 + 9 x2 = -7.071067812 + 9 Combine like terms: -7.071067812 + 9 = 1.928932188 x2 = 1.928932188 Simplifying x2 = 1.928932188 Take the square root of each side: x = {-1.388860032, 1.388860032}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.008873634, 4.008873634, -1.388860032, 1.388860032}
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