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Simplifying m4 + 8m2 + 8 = 0 Reorder the terms: 8 + 8m2 + m4 = 0 Solving 8 + 8m2 + m4 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 8m2 + -8 + m4 = 0 + -8 Reorder the terms: 8 + -8 + 8m2 + m4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 8m2 + m4 = 0 + -8 8m2 + m4 = 0 + -8 Combine like terms: 0 + -8 = -8 8m2 + m4 = -8 The m term is 8m2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8m2 + 16 + m4 = -8 + 16 Reorder the terms: 16 + 8m2 + m4 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + 8m2 + m4 = 8 Factor a perfect square on the left side: (m2 + 4)(m2 + 4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (m2 + 4) equal to 2.828427125 and -2.828427125.Subproblem 1
m2 + 4 = 2.828427125 Simplifying m2 + 4 = 2.828427125 Reorder the terms: 4 + m2 = 2.828427125 Solving 4 + m2 = 2.828427125 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m2 = 2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + m2 = 2.828427125 + -4 m2 = 2.828427125 + -4 Combine like terms: 2.828427125 + -4 = -1.171572875 m2 = -1.171572875 Simplifying m2 = -1.171572875 Reorder the terms: 1.171572875 + m2 = -1.171572875 + 1.171572875 Combine like terms: -1.171572875 + 1.171572875 = 0.000000000 1.171572875 + m2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
m2 + 4 = -2.828427125 Simplifying m2 + 4 = -2.828427125 Reorder the terms: 4 + m2 = -2.828427125 Solving 4 + m2 = -2.828427125 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m2 = -2.828427125 + -4 Combine like terms: 4 + -4 = 0 0 + m2 = -2.828427125 + -4 m2 = -2.828427125 + -4 Combine like terms: -2.828427125 + -4 = -6.828427125 m2 = -6.828427125 Simplifying m2 = -6.828427125 Reorder the terms: 6.828427125 + m2 = -6.828427125 + 6.828427125 Combine like terms: -6.828427125 + 6.828427125 = 0.000000000 6.828427125 + m2 = 0.000000000 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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