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Simplifying x4 + -32x2 + 64 = 0 Reorder the terms: 64 + -32x2 + x4 = 0 Solving 64 + -32x2 + 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 + -32x2 + -64 + x4 = 0 + -64 Reorder the terms: 64 + -64 + -32x2 + x4 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -32x2 + x4 = 0 + -64 -32x2 + x4 = 0 + -64 Combine like terms: 0 + -64 = -64 -32x2 + x4 = -64 The x term is -32x2. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x2 + 256 + x4 = -64 + 256 Reorder the terms: 256 + -32x2 + x4 = -64 + 256 Combine like terms: -64 + 256 = 192 256 + -32x2 + x4 = 192 Factor a perfect square on the left side: (x2 + -16)(x2 + -16) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x2 + -16) equal to 13.856406461 and -13.856406461.Subproblem 1
x2 + -16 = 13.856406461 Simplifying x2 + -16 = 13.856406461 Reorder the terms: -16 + x2 = 13.856406461 Solving -16 + x2 = 13.856406461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = 13.856406461 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = 13.856406461 + 16 x2 = 13.856406461 + 16 Combine like terms: 13.856406461 + 16 = 29.856406461 x2 = 29.856406461 Simplifying x2 = 29.856406461 Take the square root of each side: x = {-5.464101615, 5.464101615}Subproblem 2
x2 + -16 = -13.856406461 Simplifying x2 + -16 = -13.856406461 Reorder the terms: -16 + x2 = -13.856406461 Solving -16 + x2 = -13.856406461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x2 = -13.856406461 + 16 Combine like terms: -16 + 16 = 0 0 + x2 = -13.856406461 + 16 x2 = -13.856406461 + 16 Combine like terms: -13.856406461 + 16 = 2.143593539 x2 = 2.143593539 Simplifying x2 = 2.143593539 Take the square root of each side: x = {-1.464101615, 1.464101615}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.464101615, 5.464101615, -1.464101615, 1.464101615}
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