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Simplifying x4 + -18x2 + 34 = 0 Reorder the terms: 34 + -18x2 + x4 = 0 Solving 34 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -18x2 + -34 + x4 = 0 + -34 Reorder the terms: 34 + -34 + -18x2 + x4 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -18x2 + x4 = 0 + -34 -18x2 + x4 = 0 + -34 Combine like terms: 0 + -34 = -34 -18x2 + x4 = -34 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 = -34 + 81 Reorder the terms: 81 + -18x2 + x4 = -34 + 81 Combine like terms: -34 + 81 = 47 81 + -18x2 + x4 = 47 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x2 + -9) equal to 6.8556546 and -6.8556546.Subproblem 1
x2 + -9 = 6.8556546 Simplifying x2 + -9 = 6.8556546 Reorder the terms: -9 + x2 = 6.8556546 Solving -9 + x2 = 6.8556546 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 = 6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 6.8556546 + 9 x2 = 6.8556546 + 9 Combine like terms: 6.8556546 + 9 = 15.8556546 x2 = 15.8556546 Simplifying x2 = 15.8556546 Take the square root of each side: x = {-3.981915946, 3.981915946}Subproblem 2
x2 + -9 = -6.8556546 Simplifying x2 + -9 = -6.8556546 Reorder the terms: -9 + x2 = -6.8556546 Solving -9 + x2 = -6.8556546 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 = -6.8556546 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -6.8556546 + 9 x2 = -6.8556546 + 9 Combine like terms: -6.8556546 + 9 = 2.1443454 x2 = 2.1443454 Simplifying x2 = 2.1443454 Take the square root of each side: x = {-1.464358358, 1.464358358}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.981915946, 3.981915946, -1.464358358, 1.464358358}
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