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Simplifying 3m(m + -10) = 180 Reorder the terms: 3m(-10 + m) = 180 (-10 * 3m + m * 3m) = 180 (-30m + 3m2) = 180 Solving -30m + 3m2 = 180 Solving for variable 'm'. Reorder the terms: -180 + -30m + 3m2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -30m + 3m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + -10m + m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + -10m + m2)' equal to zero and attempt to solve: Simplifying -60 + -10m + m2 = 0 Solving -60 + -10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -10m + 60 + m2 = 0 + 60 Reorder the terms: -60 + 60 + -10m + m2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -10m + m2 = 0 + 60 -10m + m2 = 0 + 60 Combine like terms: 0 + 60 = 60 -10m + m2 = 60 The m term is -10m. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10m + 25 + m2 = 60 + 25 Reorder the terms: 25 + -10m + m2 = 60 + 25 Combine like terms: 60 + 25 = 85 25 + -10m + m2 = 85 Factor a perfect square on the left side: (m + -5)(m + -5) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (m + -5) equal to 9.219544457 and -9.219544457.Subproblem 1
m + -5 = 9.219544457 Simplifying m + -5 = 9.219544457 Reorder the terms: -5 + m = 9.219544457 Solving -5 + m = 9.219544457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 9.219544457 + 5 Combine like terms: -5 + 5 = 0 0 + m = 9.219544457 + 5 m = 9.219544457 + 5 Combine like terms: 9.219544457 + 5 = 14.219544457 m = 14.219544457 Simplifying m = 14.219544457Subproblem 2
m + -5 = -9.219544457 Simplifying m + -5 = -9.219544457 Reorder the terms: -5 + m = -9.219544457 Solving -5 + m = -9.219544457 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -9.219544457 + 5 Combine like terms: -5 + 5 = 0 0 + m = -9.219544457 + 5 m = -9.219544457 + 5 Combine like terms: -9.219544457 + 5 = -4.219544457 m = -4.219544457 Simplifying m = -4.219544457Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.219544457, -4.219544457}Solution
m = {14.219544457, -4.219544457}
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