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Simplifying x4 + -8x2 + 9 = 0 Reorder the terms: 9 + -8x2 + x4 = 0 Solving 9 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -8x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8x2 + x4 = 0 + -9 -8x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -8x2 + x4 = -9 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -9 + 16 Reorder the terms: 16 + -8x2 + x4 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8x2 + x4 = 7 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x2 + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
x2 + -4 = 2.645751311 Simplifying x2 + -4 = 2.645751311 Reorder the terms: -4 + x2 = 2.645751311 Solving -4 + x2 = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 2.645751311 + 4 x2 = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 x2 = 6.645751311 Simplifying x2 = 6.645751311 Take the square root of each side: x = {-2.577935475, 2.577935475}Subproblem 2
x2 + -4 = -2.645751311 Simplifying x2 + -4 = -2.645751311 Reorder the terms: -4 + x2 = -2.645751311 Solving -4 + x2 = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -2.645751311 + 4 x2 = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 x2 = 1.354248689 Simplifying x2 = 1.354248689 Take the square root of each side: x = {-1.163721912, 1.163721912}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.577935475, 2.577935475, -1.163721912, 1.163721912}
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