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Simplifying 2m(m + -5) + -3(m + 16) = 0 Reorder the terms: 2m(-5 + m) + -3(m + 16) = 0 (-5 * 2m + m * 2m) + -3(m + 16) = 0 (-10m + 2m2) + -3(m + 16) = 0 Reorder the terms: -10m + 2m2 + -3(16 + m) = 0 -10m + 2m2 + (16 * -3 + m * -3) = 0 -10m + 2m2 + (-48 + -3m) = 0 Reorder the terms: -48 + -10m + -3m + 2m2 = 0 Combine like terms: -10m + -3m = -13m -48 + -13m + 2m2 = 0 Solving -48 + -13m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + -6.5m + m2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -6.5m + 24 + m2 = 0 + 24 Reorder the terms: -24 + 24 + -6.5m + m2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -6.5m + m2 = 0 + 24 -6.5m + m2 = 0 + 24 Combine like terms: 0 + 24 = 24 -6.5m + m2 = 24 The m term is -6.5m. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5m + 10.5625 + m2 = 24 + 10.5625 Reorder the terms: 10.5625 + -6.5m + m2 = 24 + 10.5625 Combine like terms: 24 + 10.5625 = 34.5625 10.5625 + -6.5m + m2 = 34.5625 Factor a perfect square on the left side: (m + -3.25)(m + -3.25) = 34.5625 Calculate the square root of the right side: 5.878988008 Break this problem into two subproblems by setting (m + -3.25) equal to 5.878988008 and -5.878988008.Subproblem 1
m + -3.25 = 5.878988008 Simplifying m + -3.25 = 5.878988008 Reorder the terms: -3.25 + m = 5.878988008 Solving -3.25 + m = 5.878988008 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + m = 5.878988008 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + m = 5.878988008 + 3.25 m = 5.878988008 + 3.25 Combine like terms: 5.878988008 + 3.25 = 9.128988008 m = 9.128988008 Simplifying m = 9.128988008Subproblem 2
m + -3.25 = -5.878988008 Simplifying m + -3.25 = -5.878988008 Reorder the terms: -3.25 + m = -5.878988008 Solving -3.25 + m = -5.878988008 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + m = -5.878988008 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + m = -5.878988008 + 3.25 m = -5.878988008 + 3.25 Combine like terms: -5.878988008 + 3.25 = -2.628988008 m = -2.628988008 Simplifying m = -2.628988008Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.128988008, -2.628988008}
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