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Simplifying 4m2 + -16m + 2 = 0 Reorder the terms: 2 + -16m + 4m2 = 0 Solving 2 + -16m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -8m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -8m + 2m2)' equal to zero and attempt to solve: Simplifying 1 + -8m + 2m2 = 0 Solving 1 + -8m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -4m + m2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -4m + -0.5 + m2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -4m + m2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -4m + m2 = 0 + -0.5 -4m + m2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -4m + m2 = -0.5 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 = -0.5 + 4 Reorder the terms: 4 + -4m + m2 = -0.5 + 4 Combine like terms: -0.5 + 4 = 3.5 4 + -4m + m2 = 3.5 Factor a perfect square on the left side: (m + -2)(m + -2) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (m + -2) equal to 1.870828693 and -1.870828693.Subproblem 1
m + -2 = 1.870828693 Simplifying m + -2 = 1.870828693 Reorder the terms: -2 + m = 1.870828693 Solving -2 + m = 1.870828693 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 = 1.870828693 + 2 Combine like terms: -2 + 2 = 0 0 + m = 1.870828693 + 2 m = 1.870828693 + 2 Combine like terms: 1.870828693 + 2 = 3.870828693 m = 3.870828693 Simplifying m = 3.870828693Subproblem 2
m + -2 = -1.870828693 Simplifying m + -2 = -1.870828693 Reorder the terms: -2 + m = -1.870828693 Solving -2 + m = -1.870828693 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 = -1.870828693 + 2 Combine like terms: -2 + 2 = 0 0 + m = -1.870828693 + 2 m = -1.870828693 + 2 Combine like terms: -1.870828693 + 2 = 0.129171307 m = 0.129171307 Simplifying m = 0.129171307Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.870828693, 0.129171307}Solution
m = {3.870828693, 0.129171307}
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