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Simplifying 6m + 2(m + 7) * m = 14 Reorder the terms: 6m + 2(7 + m) * m = 14 Reorder the terms for easier multiplication: 6m + 2m(7 + m) = 14 6m + (7 * 2m + m * 2m) = 14 6m + (14m + 2m2) = 14 Combine like terms: 6m + 14m = 20m 20m + 2m2 = 14 Solving 20m + 2m2 = 14 Solving for variable 'm'. Reorder the terms: -14 + 20m + 2m2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 20m + 2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 10m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 10m + m2)' equal to zero and attempt to solve: Simplifying -7 + 10m + m2 = 0 Solving -7 + 10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 10m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + 10m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 10m + m2 = 0 + 7 10m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 10m + m2 = 7 The m term is 10m. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10m + 25 + m2 = 7 + 25 Reorder the terms: 25 + 10m + m2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + 10m + m2 = 32 Factor a perfect square on the left side: (m + 5)(m + 5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (m + 5) equal to 5.656854249 and -5.656854249.Subproblem 1
m + 5 = 5.656854249 Simplifying m + 5 = 5.656854249 Reorder the terms: 5 + m = 5.656854249 Solving 5 + m = 5.656854249 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = 5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + m = 5.656854249 + -5 m = 5.656854249 + -5 Combine like terms: 5.656854249 + -5 = 0.656854249 m = 0.656854249 Simplifying m = 0.656854249Subproblem 2
m + 5 = -5.656854249 Simplifying m + 5 = -5.656854249 Reorder the terms: 5 + m = -5.656854249 Solving 5 + m = -5.656854249 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = -5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + m = -5.656854249 + -5 m = -5.656854249 + -5 Combine like terms: -5.656854249 + -5 = -10.656854249 m = -10.656854249 Simplifying m = -10.656854249Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.656854249, -10.656854249}Solution
m = {0.656854249, -10.656854249}
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