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Simplifying x4 + 4 + -18x2 = 0 Reorder the terms: 4 + -18x2 + x4 = 0 Solving 4 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -18x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -18x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -18x2 + x4 = 0 + -4 -18x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -18x2 + x4 = -4 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 = -4 + 81 Reorder the terms: 81 + -18x2 + x4 = -4 + 81 Combine like terms: -4 + 81 = 77 81 + -18x2 + x4 = 77 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (x2 + -9) equal to 8.774964387 and -8.774964387.Subproblem 1
x2 + -9 = 8.774964387 Simplifying x2 + -9 = 8.774964387 Reorder the terms: -9 + x2 = 8.774964387 Solving -9 + x2 = 8.774964387 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 = 8.774964387 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 8.774964387 + 9 x2 = 8.774964387 + 9 Combine like terms: 8.774964387 + 9 = 17.774964387 x2 = 17.774964387 Simplifying x2 = 17.774964387 Take the square root of each side: x = {-4.216036573, 4.216036573}Subproblem 2
x2 + -9 = -8.774964387 Simplifying x2 + -9 = -8.774964387 Reorder the terms: -9 + x2 = -8.774964387 Solving -9 + x2 = -8.774964387 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 = -8.774964387 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -8.774964387 + 9 x2 = -8.774964387 + 9 Combine like terms: -8.774964387 + 9 = 0.225035613 x2 = 0.225035613 Simplifying x2 = 0.225035613 Take the square root of each side: x = {-0.474379187, 0.474379187}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.216036573, 4.216036573, -0.474379187, 0.474379187}
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