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Simplifying m6 + -4m3 + -1 = 0 Reorder the terms: -1 + -4m3 + m6 = 0 Solving -1 + -4m3 + m6 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -4m3 + 1 + m6 = 0 + 1 Reorder the terms: -1 + 1 + -4m3 + m6 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4m3 + m6 = 0 + 1 -4m3 + m6 = 0 + 1 Combine like terms: 0 + 1 = 1 -4m3 + m6 = 1 The m term is -4m3. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m3 + 4 + m6 = 1 + 4 Reorder the terms: 4 + -4m3 + m6 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4m3 + m6 = 5 Factor a perfect square on the left side: (m3 + -2)(m3 + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (m3 + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
m3 + -2 = 2.236067978 Simplifying m3 + -2 = 2.236067978 Reorder the terms: -2 + m3 = 2.236067978 Solving -2 + m3 = 2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m3 = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + m3 = 2.236067978 + 2 m3 = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 m3 = 4.236067978 Simplifying m3 = 4.236067978 Reorder the terms: -4.236067978 + m3 = 4.236067978 + -4.236067978 Combine like terms: 4.236067978 + -4.236067978 = 0.000000000 -4.236067978 + m3 = 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
m3 + -2 = -2.236067978 Simplifying m3 + -2 = -2.236067978 Reorder the terms: -2 + m3 = -2.236067978 Solving -2 + m3 = -2.236067978 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m3 = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + m3 = -2.236067978 + 2 m3 = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 m3 = -0.236067978 Simplifying m3 = -0.236067978 Reorder the terms: 0.236067978 + m3 = -0.236067978 + 0.236067978 Combine like terms: -0.236067978 + 0.236067978 = 0.000000000 0.236067978 + m3 = 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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