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Simplifying 6m + 2m(m + 7) = m + -14 Reorder the terms: 6m + 2m(7 + m) = m + -14 6m + (7 * 2m + m * 2m) = m + -14 6m + (14m + 2m2) = m + -14 Combine like terms: 6m + 14m = 20m 20m + 2m2 = m + -14 Reorder the terms: 20m + 2m2 = -14 + m Solving 20m + 2m2 = -14 + m Solving for variable 'm'. Reorder the terms: 14 + 20m + -1m + 2m2 = -14 + m + 14 + -1m Combine like terms: 20m + -1m = 19m 14 + 19m + 2m2 = -14 + m + 14 + -1m Reorder the terms: 14 + 19m + 2m2 = -14 + 14 + m + -1m Combine like terms: -14 + 14 = 0 14 + 19m + 2m2 = 0 + m + -1m 14 + 19m + 2m2 = m + -1m Combine like terms: m + -1m = 0 14 + 19m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + 9.5m + m2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 9.5m + -7 + m2 = 0 + -7 Reorder the terms: 7 + -7 + 9.5m + m2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9.5m + m2 = 0 + -7 9.5m + m2 = 0 + -7 Combine like terms: 0 + -7 = -7 9.5m + m2 = -7 The m term is 9.5m. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5m + 22.5625 + m2 = -7 + 22.5625 Reorder the terms: 22.5625 + 9.5m + m2 = -7 + 22.5625 Combine like terms: -7 + 22.5625 = 15.5625 22.5625 + 9.5m + m2 = 15.5625 Factor a perfect square on the left side: (m + 4.75)(m + 4.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (m + 4.75) equal to 3.94493346 and -3.94493346.Subproblem 1
m + 4.75 = 3.94493346 Simplifying m + 4.75 = 3.94493346 Reorder the terms: 4.75 + m = 3.94493346 Solving 4.75 + m = 3.94493346 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + m = 3.94493346 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + m = 3.94493346 + -4.75 m = 3.94493346 + -4.75 Combine like terms: 3.94493346 + -4.75 = -0.80506654 m = -0.80506654 Simplifying m = -0.80506654Subproblem 2
m + 4.75 = -3.94493346 Simplifying m + 4.75 = -3.94493346 Reorder the terms: 4.75 + m = -3.94493346 Solving 4.75 + m = -3.94493346 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + m = -3.94493346 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + m = -3.94493346 + -4.75 m = -3.94493346 + -4.75 Combine like terms: -3.94493346 + -4.75 = -8.69493346 m = -8.69493346 Simplifying m = -8.69493346Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.80506654, -8.69493346}
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