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Simplifying x4 + -18x2 + 16 = 0 Reorder the terms: 16 + -18x2 + x4 = 0 Solving 16 + -18x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -18x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + -18x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -18x2 + x4 = 0 + -16 -18x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 -18x2 + x4 = -16 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 = -16 + 81 Reorder the terms: 81 + -18x2 + x4 = -16 + 81 Combine like terms: -16 + 81 = 65 81 + -18x2 + x4 = 65 Factor a perfect square on the left side: (x2 + -9)(x2 + -9) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x2 + -9) equal to 8.062257748 and -8.062257748.Subproblem 1
x2 + -9 = 8.062257748 Simplifying x2 + -9 = 8.062257748 Reorder the terms: -9 + x2 = 8.062257748 Solving -9 + x2 = 8.062257748 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 = 8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = 8.062257748 + 9 x2 = 8.062257748 + 9 Combine like terms: 8.062257748 + 9 = 17.062257748 x2 = 17.062257748 Simplifying x2 = 17.062257748 Take the square root of each side: x = {-4.130648587, 4.130648587}Subproblem 2
x2 + -9 = -8.062257748 Simplifying x2 + -9 = -8.062257748 Reorder the terms: -9 + x2 = -8.062257748 Solving -9 + x2 = -8.062257748 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 = -8.062257748 + 9 Combine like terms: -9 + 9 = 0 0 + x2 = -8.062257748 + 9 x2 = -8.062257748 + 9 Combine like terms: -8.062257748 + 9 = 0.937742252 x2 = 0.937742252 Simplifying x2 = 0.937742252 Take the square root of each side: x = {-0.968370927, 0.968370927}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.130648587, 4.130648587, -0.968370927, 0.968370927}
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