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Simplifying 7(7 + 5m) + m(m + 6) * 4 = 0 (7 * 7 + 5m * 7) + m(m + 6) * 4 = 0 (49 + 35m) + m(m + 6) * 4 = 0 Reorder the terms: 49 + 35m + m(6 + m) * 4 = 0 Reorder the terms for easier multiplication: 49 + 35m + 4m(6 + m) = 0 49 + 35m + (6 * 4m + m * 4m) = 0 49 + 35m + (24m + 4m2) = 0 Combine like terms: 35m + 24m = 59m 49 + 59m + 4m2 = 0 Solving 49 + 59m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 12.25 + 14.75m + m2 = 0 Move the constant term to the right: Add '-12.25' to each side of the equation. 12.25 + 14.75m + -12.25 + m2 = 0 + -12.25 Reorder the terms: 12.25 + -12.25 + 14.75m + m2 = 0 + -12.25 Combine like terms: 12.25 + -12.25 = 0.00 0.00 + 14.75m + m2 = 0 + -12.25 14.75m + m2 = 0 + -12.25 Combine like terms: 0 + -12.25 = -12.25 14.75m + m2 = -12.25 The m term is 14.75m. Take half its coefficient (7.375). Square it (54.390625) and add it to both sides. Add '54.390625' to each side of the equation. 14.75m + 54.390625 + m2 = -12.25 + 54.390625 Reorder the terms: 54.390625 + 14.75m + m2 = -12.25 + 54.390625 Combine like terms: -12.25 + 54.390625 = 42.140625 54.390625 + 14.75m + m2 = 42.140625 Factor a perfect square on the left side: (m + 7.375)(m + 7.375) = 42.140625 Calculate the square root of the right side: 6.491581086 Break this problem into two subproblems by setting (m + 7.375) equal to 6.491581086 and -6.491581086.Subproblem 1
m + 7.375 = 6.491581086 Simplifying m + 7.375 = 6.491581086 Reorder the terms: 7.375 + m = 6.491581086 Solving 7.375 + m = 6.491581086 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7.375' to each side of the equation. 7.375 + -7.375 + m = 6.491581086 + -7.375 Combine like terms: 7.375 + -7.375 = 0.000 0.000 + m = 6.491581086 + -7.375 m = 6.491581086 + -7.375 Combine like terms: 6.491581086 + -7.375 = -0.883418914 m = -0.883418914 Simplifying m = -0.883418914Subproblem 2
m + 7.375 = -6.491581086 Simplifying m + 7.375 = -6.491581086 Reorder the terms: 7.375 + m = -6.491581086 Solving 7.375 + m = -6.491581086 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7.375' to each side of the equation. 7.375 + -7.375 + m = -6.491581086 + -7.375 Combine like terms: 7.375 + -7.375 = 0.000 0.000 + m = -6.491581086 + -7.375 m = -6.491581086 + -7.375 Combine like terms: -6.491581086 + -7.375 = -13.866581086 m = -13.866581086 Simplifying m = -13.866581086Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.883418914, -13.866581086}
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