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Simplifying x4 + -16x2 + 36 = 0 Reorder the terms: 36 + -16x2 + x4 = 0 Solving 36 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -16x2 + -36 + x4 = 0 + -36 Reorder the terms: 36 + -36 + -16x2 + x4 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16x2 + x4 = 0 + -36 -16x2 + x4 = 0 + -36 Combine like terms: 0 + -36 = -36 -16x2 + x4 = -36 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = -36 + 64 Reorder the terms: 64 + -16x2 + x4 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + -16x2 + x4 = 28 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x2 + -8) equal to 5.291502622 and -5.291502622.Subproblem 1
x2 + -8 = 5.291502622 Simplifying x2 + -8 = 5.291502622 Reorder the terms: -8 + x2 = 5.291502622 Solving -8 + x2 = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 5.291502622 + 8 x2 = 5.291502622 + 8 Combine like terms: 5.291502622 + 8 = 13.291502622 x2 = 13.291502622 Simplifying x2 = 13.291502622 Take the square root of each side: x = {-3.645751311, 3.645751311}Subproblem 2
x2 + -8 = -5.291502622 Simplifying x2 + -8 = -5.291502622 Reorder the terms: -8 + x2 = -5.291502622 Solving -8 + x2 = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -5.291502622 + 8 x2 = -5.291502622 + 8 Combine like terms: -5.291502622 + 8 = 2.708497378 x2 = 2.708497378 Simplifying x2 = 2.708497378 Take the square root of each side: x = {-1.645751311, 1.645751311}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.645751311, 3.645751311, -1.645751311, 1.645751311}
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