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Simplifying 0 = m2 + -49 + 14m Reorder the terms: 0 = -49 + 14m + m2 Solving 0 = -49 + 14m + m2 Solving for variable 'm'. Combine like terms: 0 + 49 = 49 49 + -14m + -1m2 = -49 + 14m + m2 + 49 + -14m + -1m2 Reorder the terms: 49 + -14m + -1m2 = -49 + 49 + 14m + -14m + m2 + -1m2 Combine like terms: -49 + 49 = 0 49 + -14m + -1m2 = 0 + 14m + -14m + m2 + -1m2 49 + -14m + -1m2 = 14m + -14m + m2 + -1m2 Combine like terms: 14m + -14m = 0 49 + -14m + -1m2 = 0 + m2 + -1m2 49 + -14m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 49 + -14m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 14m + m2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 14m + 49 + m2 = 0 + 49 Reorder the terms: -49 + 49 + 14m + m2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 14m + m2 = 0 + 49 14m + m2 = 0 + 49 Combine like terms: 0 + 49 = 49 14m + m2 = 49 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 = 49 + 49 Reorder the terms: 49 + 14m + m2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + 14m + m2 = 98 Factor a perfect square on the left side: (m + 7)(m + 7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (m + 7) equal to 9.899494937 and -9.899494937.Subproblem 1
m + 7 = 9.899494937 Simplifying m + 7 = 9.899494937 Reorder the terms: 7 + m = 9.899494937 Solving 7 + m = 9.899494937 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 = 9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + m = 9.899494937 + -7 m = 9.899494937 + -7 Combine like terms: 9.899494937 + -7 = 2.899494937 m = 2.899494937 Simplifying m = 2.899494937Subproblem 2
m + 7 = -9.899494937 Simplifying m + 7 = -9.899494937 Reorder the terms: 7 + m = -9.899494937 Solving 7 + m = -9.899494937 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 = -9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + m = -9.899494937 + -7 m = -9.899494937 + -7 Combine like terms: -9.899494937 + -7 = -16.899494937 m = -16.899494937 Simplifying m = -16.899494937Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.899494937, -16.899494937}
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