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Simplifying 4m2 + -16m + -4 = 0 Reorder the terms: -4 + -16m + 4m2 = 0 Solving -4 + -16m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -4m + m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -4m + m2)' equal to zero and attempt to solve: Simplifying -1 + -4m + m2 = 0 Solving -1 + -4m + m2 = 0 Begin completing the square. 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 = 4.236067978 m = 4.236067978 Simplifying m = 4.236067978Subproblem 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 = -0.236067978 m = -0.236067978 Simplifying m = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.236067978, -0.236067978}Solution
m = {4.236067978, -0.236067978}
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