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Simplifying m + 2m(m + 10) = 180 Reorder the terms: m + 2m(10 + m) = 180 m + (10 * 2m + m * 2m) = 180 m + (20m + 2m2) = 180 Combine like terms: m + 20m = 21m 21m + 2m2 = 180 Solving 21m + 2m2 = 180 Solving for variable 'm'. Reorder the terms: -180 + 21m + 2m2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 21m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -90 + 10.5m + m2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 10.5m + 90 + m2 = 0 + 90 Reorder the terms: -90 + 90 + 10.5m + m2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 10.5m + m2 = 0 + 90 10.5m + m2 = 0 + 90 Combine like terms: 0 + 90 = 90 10.5m + m2 = 90 The m term is 10.5m. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5m + 27.5625 + m2 = 90 + 27.5625 Reorder the terms: 27.5625 + 10.5m + m2 = 90 + 27.5625 Combine like terms: 90 + 27.5625 = 117.5625 27.5625 + 10.5m + m2 = 117.5625 Factor a perfect square on the left side: (m + 5.25)(m + 5.25) = 117.5625 Calculate the square root of the right side: 10.842624221 Break this problem into two subproblems by setting (m + 5.25) equal to 10.842624221 and -10.842624221.Subproblem 1
m + 5.25 = 10.842624221 Simplifying m + 5.25 = 10.842624221 Reorder the terms: 5.25 + m = 10.842624221 Solving 5.25 + m = 10.842624221 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + m = 10.842624221 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + m = 10.842624221 + -5.25 m = 10.842624221 + -5.25 Combine like terms: 10.842624221 + -5.25 = 5.592624221 m = 5.592624221 Simplifying m = 5.592624221Subproblem 2
m + 5.25 = -10.842624221 Simplifying m + 5.25 = -10.842624221 Reorder the terms: 5.25 + m = -10.842624221 Solving 5.25 + m = -10.842624221 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + m = -10.842624221 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + m = -10.842624221 + -5.25 m = -10.842624221 + -5.25 Combine like terms: -10.842624221 + -5.25 = -16.092624221 m = -16.092624221 Simplifying m = -16.092624221Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.592624221, -16.092624221}
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