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Simplifying 4m2 + -16m + -50 = 0 Reorder the terms: -50 + -16m + 4m2 = 0 Solving -50 + -16m + 4m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -8m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -8m + 2m2)' equal to zero and attempt to solve: Simplifying -25 + -8m + 2m2 = 0 Solving -25 + -8m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -4m + m2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -4m + 12.5 + m2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -4m + m2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -4m + m2 = 0 + 12.5 -4m + m2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -4m + m2 = 12.5 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 = 12.5 + 4 Reorder the terms: 4 + -4m + m2 = 12.5 + 4 Combine like terms: 12.5 + 4 = 16.5 4 + -4m + m2 = 16.5 Factor a perfect square on the left side: (m + -2)(m + -2) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (m + -2) equal to 4.062019202 and -4.062019202.Subproblem 1
m + -2 = 4.062019202 Simplifying m + -2 = 4.062019202 Reorder the terms: -2 + m = 4.062019202 Solving -2 + m = 4.062019202 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 = 4.062019202 + 2 Combine like terms: -2 + 2 = 0 0 + m = 4.062019202 + 2 m = 4.062019202 + 2 Combine like terms: 4.062019202 + 2 = 6.062019202 m = 6.062019202 Simplifying m = 6.062019202Subproblem 2
m + -2 = -4.062019202 Simplifying m + -2 = -4.062019202 Reorder the terms: -2 + m = -4.062019202 Solving -2 + m = -4.062019202 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 = -4.062019202 + 2 Combine like terms: -2 + 2 = 0 0 + m = -4.062019202 + 2 m = -4.062019202 + 2 Combine like terms: -4.062019202 + 2 = -2.062019202 m = -2.062019202 Simplifying m = -2.062019202Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.062019202, -2.062019202}Solution
m = {6.062019202, -2.062019202}
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