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Simplifying 50m2 + -20m + -2 = 0 Reorder the terms: -2 + -20m + 50m2 = 0 Solving -2 + -20m + 50m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -10m + 25m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -10m + 25m2)' equal to zero and attempt to solve: Simplifying -1 + -10m + 25m2 = 0 Solving -1 + -10m + 25m2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -0.4m + m2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.4m + 0.04 + m2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.4m + m2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.4m + m2 = 0 + 0.04 -0.4m + m2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.4m + m2 = 0.04 The m term is -0.4m. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4m + 0.04 + m2 = 0.04 + 0.04 Reorder the terms: 0.04 + -0.4m + m2 = 0.04 + 0.04 Combine like terms: 0.04 + 0.04 = 0.08 0.04 + -0.4m + m2 = 0.08 Factor a perfect square on the left side: (m + -0.2)(m + -0.2) = 0.08 Calculate the square root of the right side: 0.282842712 Break this problem into two subproblems by setting (m + -0.2) equal to 0.282842712 and -0.282842712.Subproblem 1
m + -0.2 = 0.282842712 Simplifying m + -0.2 = 0.282842712 Reorder the terms: -0.2 + m = 0.282842712 Solving -0.2 + m = 0.282842712 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = 0.282842712 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = 0.282842712 + 0.2 m = 0.282842712 + 0.2 Combine like terms: 0.282842712 + 0.2 = 0.482842712 m = 0.482842712 Simplifying m = 0.482842712Subproblem 2
m + -0.2 = -0.282842712 Simplifying m + -0.2 = -0.282842712 Reorder the terms: -0.2 + m = -0.282842712 Solving -0.2 + m = -0.282842712 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = -0.282842712 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = -0.282842712 + 0.2 m = -0.282842712 + 0.2 Combine like terms: -0.282842712 + 0.2 = -0.082842712 m = -0.082842712 Simplifying m = -0.082842712Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.482842712, -0.082842712}Solution
m = {0.482842712, -0.082842712}
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