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Simplifying 4m2 + -16m + -40 = 0 Reorder the terms: -40 + -16m + 4m2 = 0 Solving -40 + -16m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -4m + m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + -4m + m2)' equal to zero and attempt to solve: Simplifying -10 + -4m + m2 = 0 Solving -10 + -4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -4m + 10 + m2 = 0 + 10 Reorder the terms: -10 + 10 + -4m + m2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4m + m2 = 0 + 10 -4m + m2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4m + m2 = 10 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 = 10 + 4 Reorder the terms: 4 + -4m + m2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4m + m2 = 14 Factor a perfect square on the left side: (m + -2)(m + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (m + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
m + -2 = 3.741657387 Simplifying m + -2 = 3.741657387 Reorder the terms: -2 + m = 3.741657387 Solving -2 + m = 3.741657387 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 = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + m = 3.741657387 + 2 m = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 m = 5.741657387 Simplifying m = 5.741657387Subproblem 2
m + -2 = -3.741657387 Simplifying m + -2 = -3.741657387 Reorder the terms: -2 + m = -3.741657387 Solving -2 + m = -3.741657387 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 = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + m = -3.741657387 + 2 m = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 m = -1.741657387 Simplifying m = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.741657387, -1.741657387}Solution
m = {5.741657387, -1.741657387}
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