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Simplifying x4 + -18x2 + 67 = 0 Reorder the terms: 67 + -18x2 + x4 = 0 Solving 67 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-67' to each side of the equation. 67 + -18x2 + -67 + x4 = 0 + -67 Reorder the terms: 67 + -67 + -18x2 + x4 = 0 + -67 Combine like terms: 67 + -67 = 0 0 + -18x2 + x4 = 0 + -67 -18x2 + x4 = 0 + -67 Combine like terms: 0 + -67 = -67 -18x2 + x4 = -67 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 = -67 + 81 Reorder the terms: 81 + -18x2 + x4 = -67 + 81 Combine like terms: -67 + 81 = 14 81 + -18x2 + x4 = 14 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x2 + -9) equal to 3.741657387 and -3.741657387.Subproblem 1
x2 + -9 = 3.741657387 Simplifying x2 + -9 = 3.741657387 Reorder the terms: -9 + x2 = 3.741657387 Solving -9 + x2 = 3.741657387 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 = 3.741657387 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 3.741657387 + 9 x2 = 3.741657387 + 9 Combine like terms: 3.741657387 + 9 = 12.741657387 x2 = 12.741657387 Simplifying x2 = 12.741657387 Take the square root of each side: x = {-3.569545824, 3.569545824}Subproblem 2
x2 + -9 = -3.741657387 Simplifying x2 + -9 = -3.741657387 Reorder the terms: -9 + x2 = -3.741657387 Solving -9 + x2 = -3.741657387 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 = -3.741657387 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -3.741657387 + 9 x2 = -3.741657387 + 9 Combine like terms: -3.741657387 + 9 = 5.258342613 x2 = 5.258342613 Simplifying x2 = 5.258342613 Take the square root of each side: x = {-2.293107632, 2.293107632}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.569545824, 3.569545824, -2.293107632, 2.293107632}
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