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Simplifying m4 + -18m2 = 81 Reorder the terms: -18m2 + m4 = 81 Solving -18m2 + m4 = 81 Solving for variable 'm'. Reorder the terms: -81 + -18m2 + m4 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + -18m2 + m4 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -18m2 + 81 + m4 = 0 + 81 Reorder the terms: -81 + 81 + -18m2 + m4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -18m2 + m4 = 0 + 81 -18m2 + m4 = 0 + 81 Combine like terms: 0 + 81 = 81 -18m2 + m4 = 81 The m term is -18m2. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18m2 + 81 + m4 = 81 + 81 Reorder the terms: 81 + -18m2 + m4 = 81 + 81 Combine like terms: 81 + 81 = 162 81 + -18m2 + m4 = 162 Factor a perfect square on the left side: (m2 + -9)(m2 + -9) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (m2 + -9) equal to 12.727922061 and -12.727922061.Subproblem 1
m2 + -9 = 12.727922061 Simplifying m2 + -9 = 12.727922061 Reorder the terms: -9 + m2 = 12.727922061 Solving -9 + m2 = 12.727922061 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + m2 = 12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + m2 = 12.727922061 + 9 m2 = 12.727922061 + 9 Combine like terms: 12.727922061 + 9 = 21.727922061 m2 = 21.727922061 Simplifying m2 = 21.727922061 Take the square root of each side: m = {-4.661321922, 4.661321922}Subproblem 2
m2 + -9 = -12.727922061 Simplifying m2 + -9 = -12.727922061 Reorder the terms: -9 + m2 = -12.727922061 Solving -9 + m2 = -12.727922061 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + m2 = -12.727922061 + 9 Combine like terms: -9 + 9 = 0 0 + m2 = -12.727922061 + 9 m2 = -12.727922061 + 9 Combine like terms: -12.727922061 + 9 = -3.727922061 m2 = -3.727922061 Simplifying m2 = -3.727922061 Reorder the terms: 3.727922061 + m2 = -3.727922061 + 3.727922061 Combine like terms: -3.727922061 + 3.727922061 = 0.000000000 3.727922061 + 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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