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Simplifying x4 + -18x2 + 64 = 0 Reorder the terms: 64 + -18x2 + x4 = 0 Solving 64 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -18x2 + -64 + x4 = 0 + -64 Reorder the terms: 64 + -64 + -18x2 + x4 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -18x2 + x4 = 0 + -64 -18x2 + x4 = 0 + -64 Combine like terms: 0 + -64 = -64 -18x2 + x4 = -64 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 = -64 + 81 Reorder the terms: 81 + -18x2 + x4 = -64 + 81 Combine like terms: -64 + 81 = 17 81 + -18x2 + x4 = 17 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x2 + -9) equal to 4.123105626 and -4.123105626.Subproblem 1
x2 + -9 = 4.123105626 Simplifying x2 + -9 = 4.123105626 Reorder the terms: -9 + x2 = 4.123105626 Solving -9 + x2 = 4.123105626 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 = 4.123105626 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 4.123105626 + 9 x2 = 4.123105626 + 9 Combine like terms: 4.123105626 + 9 = 13.123105626 x2 = 13.123105626 Simplifying x2 = 13.123105626 Take the square root of each side: x = {-3.622582729, 3.622582729}Subproblem 2
x2 + -9 = -4.123105626 Simplifying x2 + -9 = -4.123105626 Reorder the terms: -9 + x2 = -4.123105626 Solving -9 + x2 = -4.123105626 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 = -4.123105626 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -4.123105626 + 9 x2 = -4.123105626 + 9 Combine like terms: -4.123105626 + 9 = 4.876894374 x2 = 4.876894374 Simplifying x2 = 4.876894374 Take the square root of each side: x = {-2.208369166, 2.208369166}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.622582729, 3.622582729, -2.208369166, 2.208369166}
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