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Simplifying 2m2 + 56m + -7 = 0 Reorder the terms: -7 + 56m + 2m2 = 0 Solving -7 + 56m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 28m + m2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 28m + 3.5 + m2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 28m + m2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 28m + m2 = 0 + 3.5 28m + m2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 28m + m2 = 3.5 The m term is 28m. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28m + 196 + m2 = 3.5 + 196 Reorder the terms: 196 + 28m + m2 = 3.5 + 196 Combine like terms: 3.5 + 196 = 199.5 196 + 28m + m2 = 199.5 Factor a perfect square on the left side: (m + 14)(m + 14) = 199.5 Calculate the square root of the right side: 14.124446892 Break this problem into two subproblems by setting (m + 14) equal to 14.124446892 and -14.124446892.Subproblem 1
m + 14 = 14.124446892 Simplifying m + 14 = 14.124446892 Reorder the terms: 14 + m = 14.124446892 Solving 14 + m = 14.124446892 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + m = 14.124446892 + -14 Combine like terms: 14 + -14 = 0 0 + m = 14.124446892 + -14 m = 14.124446892 + -14 Combine like terms: 14.124446892 + -14 = 0.124446892 m = 0.124446892 Simplifying m = 0.124446892Subproblem 2
m + 14 = -14.124446892 Simplifying m + 14 = -14.124446892 Reorder the terms: 14 + m = -14.124446892 Solving 14 + m = -14.124446892 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + m = -14.124446892 + -14 Combine like terms: 14 + -14 = 0 0 + m = -14.124446892 + -14 m = -14.124446892 + -14 Combine like terms: -14.124446892 + -14 = -28.124446892 m = -28.124446892 Simplifying m = -28.124446892Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.124446892, -28.124446892}
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