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Simplifying m2 + 14m + 49 = 20 Reorder the terms: 49 + 14m + m2 = 20 Solving 49 + 14m + m2 = 20 Solving for variable 'm'. Reorder the terms: 49 + -20 + 14m + m2 = 20 + -20 Combine like terms: 49 + -20 = 29 29 + 14m + m2 = 20 + -20 Combine like terms: 20 + -20 = 0 29 + 14m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 14m + -29 + m2 = 0 + -29 Reorder the terms: 29 + -29 + 14m + m2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 14m + m2 = 0 + -29 14m + m2 = 0 + -29 Combine like terms: 0 + -29 = -29 14m + m2 = -29 The m term is 14m. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14m + 49 + m2 = -29 + 49 Reorder the terms: 49 + 14m + m2 = -29 + 49 Combine like terms: -29 + 49 = 20 49 + 14m + m2 = 20 Factor a perfect square on the left side: (m + 7)(m + 7) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (m + 7) equal to 4.472135955 and -4.472135955.Subproblem 1
m + 7 = 4.472135955 Simplifying m + 7 = 4.472135955 Reorder the terms: 7 + m = 4.472135955 Solving 7 + m = 4.472135955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = 4.472135955 + -7 Combine like terms: 7 + -7 = 0 0 + m = 4.472135955 + -7 m = 4.472135955 + -7 Combine like terms: 4.472135955 + -7 = -2.527864045 m = -2.527864045 Simplifying m = -2.527864045Subproblem 2
m + 7 = -4.472135955 Simplifying m + 7 = -4.472135955 Reorder the terms: 7 + m = -4.472135955 Solving 7 + m = -4.472135955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = -4.472135955 + -7 Combine like terms: 7 + -7 = 0 0 + m = -4.472135955 + -7 m = -4.472135955 + -7 Combine like terms: -4.472135955 + -7 = -11.472135955 m = -11.472135955 Simplifying m = -11.472135955Solution
The solution to the problem is based on the solutions from the subproblems. m = {-2.527864045, -11.472135955}
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