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Simplifying 0 = x4 + -18x2 + 9 Reorder the terms: 0 = 9 + -18x2 + x4 Solving 0 = 9 + -18x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + 18x2 + -1x4 = 9 + -18x2 + x4 + -9 + 18x2 + -1x4 Reorder the terms: -9 + 18x2 + -1x4 = 9 + -9 + -18x2 + 18x2 + x4 + -1x4 Combine like terms: 9 + -9 = 0 -9 + 18x2 + -1x4 = 0 + -18x2 + 18x2 + x4 + -1x4 -9 + 18x2 + -1x4 = -18x2 + 18x2 + x4 + -1x4 Combine like terms: -18x2 + 18x2 = 0 -9 + 18x2 + -1x4 = 0 + x4 + -1x4 -9 + 18x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -9 + 18x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -18x2 + x4 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -18x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -18x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -18x2 + x4 = 0 + -9 -18x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -18x2 + x4 = -9 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 = -9 + 81 Reorder the terms: 81 + -18x2 + x4 = -9 + 81 Combine like terms: -9 + 81 = 72 81 + -18x2 + x4 = 72 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x2 + -9) equal to 8.485281374 and -8.485281374.Subproblem 1
x2 + -9 = 8.485281374 Simplifying x2 + -9 = 8.485281374 Reorder the terms: -9 + x2 = 8.485281374 Solving -9 + x2 = 8.485281374 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 = 8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 8.485281374 + 9 x2 = 8.485281374 + 9 Combine like terms: 8.485281374 + 9 = 17.485281374 x2 = 17.485281374 Simplifying x2 = 17.485281374 Take the square root of each side: x = {-4.18154055, 4.18154055}Subproblem 2
x2 + -9 = -8.485281374 Simplifying x2 + -9 = -8.485281374 Reorder the terms: -9 + x2 = -8.485281374 Solving -9 + x2 = -8.485281374 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 = -8.485281374 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -8.485281374 + 9 x2 = -8.485281374 + 9 Combine like terms: -8.485281374 + 9 = 0.514718626 x2 = 0.514718626 Simplifying x2 = 0.514718626 Take the square root of each side: x = {-0.717438935, 0.717438935}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.18154055, 4.18154055, -0.717438935, 0.717438935}
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