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Simplifying x4 + 72x2 + 64 = 0 Reorder the terms: 64 + 72x2 + x4 = 0 Solving 64 + 72x2 + 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 + 72x2 + -64 + x4 = 0 + -64 Reorder the terms: 64 + -64 + 72x2 + x4 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 72x2 + x4 = 0 + -64 72x2 + x4 = 0 + -64 Combine like terms: 0 + -64 = -64 72x2 + x4 = -64 The x term is 72x2. Take half its coefficient (36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. 72x2 + 1296 + x4 = -64 + 1296 Reorder the terms: 1296 + 72x2 + x4 = -64 + 1296 Combine like terms: -64 + 1296 = 1232 1296 + 72x2 + x4 = 1232 Factor a perfect square on the left side: (x2 + 36)(x2 + 36) = 1232 Calculate the square root of the right side: 35.09985755 Break this problem into two subproblems by setting (x2 + 36) equal to 35.09985755 and -35.09985755.Subproblem 1
x2 + 36 = 35.09985755 Simplifying x2 + 36 = 35.09985755 Reorder the terms: 36 + x2 = 35.09985755 Solving 36 + x2 = 35.09985755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x2 = 35.09985755 + -36 Combine like terms: 36 + -36 = 0 0 + x2 = 35.09985755 + -36 x2 = 35.09985755 + -36 Combine like terms: 35.09985755 + -36 = -0.90014245 x2 = -0.90014245 Simplifying x2 = -0.90014245 Reorder the terms: 0.90014245 + x2 = -0.90014245 + 0.90014245 Combine like terms: -0.90014245 + 0.90014245 = 0.00000000 0.90014245 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 36 = -35.09985755 Simplifying x2 + 36 = -35.09985755 Reorder the terms: 36 + x2 = -35.09985755 Solving 36 + x2 = -35.09985755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -36 + x2 = -35.09985755 + -36 Combine like terms: 36 + -36 = 0 0 + x2 = -35.09985755 + -36 x2 = -35.09985755 + -36 Combine like terms: -35.09985755 + -36 = -71.09985755 x2 = -71.09985755 Simplifying x2 = -71.09985755 Reorder the terms: 71.09985755 + x2 = -71.09985755 + 71.09985755 Combine like terms: -71.09985755 + 71.09985755 = 0.00000000 71.09985755 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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