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Simplifying x4 + -18x2 + 40 = 0 Reorder the terms: 40 + -18x2 + x4 = 0 Solving 40 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -18x2 + -40 + x4 = 0 + -40 Reorder the terms: 40 + -40 + -18x2 + x4 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -18x2 + x4 = 0 + -40 -18x2 + x4 = 0 + -40 Combine like terms: 0 + -40 = -40 -18x2 + x4 = -40 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 = -40 + 81 Reorder the terms: 81 + -18x2 + x4 = -40 + 81 Combine like terms: -40 + 81 = 41 81 + -18x2 + x4 = 41 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x2 + -9) equal to 6.403124237 and -6.403124237.Subproblem 1
x2 + -9 = 6.403124237 Simplifying x2 + -9 = 6.403124237 Reorder the terms: -9 + x2 = 6.403124237 Solving -9 + x2 = 6.403124237 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 = 6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 6.403124237 + 9 x2 = 6.403124237 + 9 Combine like terms: 6.403124237 + 9 = 15.403124237 x2 = 15.403124237 Simplifying x2 = 15.403124237 Take the square root of each side: x = {-3.924681419, 3.924681419}Subproblem 2
x2 + -9 = -6.403124237 Simplifying x2 + -9 = -6.403124237 Reorder the terms: -9 + x2 = -6.403124237 Solving -9 + x2 = -6.403124237 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 = -6.403124237 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -6.403124237 + 9 x2 = -6.403124237 + 9 Combine like terms: -6.403124237 + 9 = 2.596875763 x2 = 2.596875763 Simplifying x2 = 2.596875763 Take the square root of each side: x = {-1.611482474, 1.611482474}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.924681419, 3.924681419, -1.611482474, 1.611482474}
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