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Simplifying -3m(m2 + 4m + -1) = 0 Reorder the terms: -3m(-1 + 4m + m2) = 0 (-1 * -3m + 4m * -3m + m2 * -3m) = 0 (3m + -12m2 + -3m3) = 0 Solving 3m + -12m2 + -3m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3m'. 3m(1 + -4m + -1m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(1 + -4m + -1m2)' equal to zero and attempt to solve: Simplifying 1 + -4m + -1m2 = 0 Solving 1 + -4m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 4m + m2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 4m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + 4m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4m + m2 = 0 + 1 4m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 4m + m2 = 1 The m term is 4m. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m + 4 + m2 = 1 + 4 Reorder the terms: 4 + 4m + m2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + 4m + m2 = 5 Factor a perfect square on the left side: (m + 2)(m + 2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (m + 2) equal to 2.236067978 and -2.236067978.Subproblem 1
m + 2 = 2.236067978 Simplifying m + 2 = 2.236067978 Reorder the terms: 2 + m = 2.236067978 Solving 2 + m = 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 + m = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + m = 2.236067978 + -2 m = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 m = 0.236067978 Simplifying m = 0.236067978Subproblem 2
m + 2 = -2.236067978 Simplifying m + 2 = -2.236067978 Reorder the terms: 2 + m = -2.236067978 Solving 2 + m = -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 + m = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + m = -2.236067978 + -2 m = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 m = -4.236067978 Simplifying m = -4.236067978Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.236067978, -4.236067978}Solution
m = {0, 0.236067978, -4.236067978}
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