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Simplifying 2m(m + 5) = 47 Reorder the terms: 2m(5 + m) = 47 (5 * 2m + m * 2m) = 47 (10m + 2m2) = 47 Solving 10m + 2m2 = 47 Solving for variable 'm'. Reorder the terms: -47 + 10m + 2m2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 10m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23.5 + 5m + m2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + 5m + 23.5 + m2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + 5m + m2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + 5m + m2 = 0 + 23.5 5m + m2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 5m + m2 = 23.5 The m term is 5m. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5m + 6.25 + m2 = 23.5 + 6.25 Reorder the terms: 6.25 + 5m + m2 = 23.5 + 6.25 Combine like terms: 23.5 + 6.25 = 29.75 6.25 + 5m + m2 = 29.75 Factor a perfect square on the left side: (m + 2.5)(m + 2.5) = 29.75 Calculate the square root of the right side: 5.454356057 Break this problem into two subproblems by setting (m + 2.5) equal to 5.454356057 and -5.454356057.Subproblem 1
m + 2.5 = 5.454356057 Simplifying m + 2.5 = 5.454356057 Reorder the terms: 2.5 + m = 5.454356057 Solving 2.5 + m = 5.454356057 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = 5.454356057 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = 5.454356057 + -2.5 m = 5.454356057 + -2.5 Combine like terms: 5.454356057 + -2.5 = 2.954356057 m = 2.954356057 Simplifying m = 2.954356057Subproblem 2
m + 2.5 = -5.454356057 Simplifying m + 2.5 = -5.454356057 Reorder the terms: 2.5 + m = -5.454356057 Solving 2.5 + m = -5.454356057 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = -5.454356057 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = -5.454356057 + -2.5 m = -5.454356057 + -2.5 Combine like terms: -5.454356057 + -2.5 = -7.954356057 m = -7.954356057 Simplifying m = -7.954356057Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.954356057, -7.954356057}
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