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Simplifying m2 + 28m = -39 Reorder the terms: 28m + m2 = -39 Solving 28m + m2 = -39 Solving for variable 'm'. Reorder the terms: 39 + 28m + m2 = -39 + 39 Combine like terms: -39 + 39 = 0 39 + 28m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 28m + -39 + m2 = 0 + -39 Reorder the terms: 39 + -39 + 28m + m2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 28m + m2 = 0 + -39 28m + m2 = 0 + -39 Combine like terms: 0 + -39 = -39 28m + m2 = -39 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 = -39 + 196 Reorder the terms: 196 + 28m + m2 = -39 + 196 Combine like terms: -39 + 196 = 157 196 + 28m + m2 = 157 Factor a perfect square on the left side: (m + 14)(m + 14) = 157 Calculate the square root of the right side: 12.529964086 Break this problem into two subproblems by setting (m + 14) equal to 12.529964086 and -12.529964086.Subproblem 1
m + 14 = 12.529964086 Simplifying m + 14 = 12.529964086 Reorder the terms: 14 + m = 12.529964086 Solving 14 + m = 12.529964086 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 = 12.529964086 + -14 Combine like terms: 14 + -14 = 0 0 + m = 12.529964086 + -14 m = 12.529964086 + -14 Combine like terms: 12.529964086 + -14 = -1.470035914 m = -1.470035914 Simplifying m = -1.470035914Subproblem 2
m + 14 = -12.529964086 Simplifying m + 14 = -12.529964086 Reorder the terms: 14 + m = -12.529964086 Solving 14 + m = -12.529964086 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 = -12.529964086 + -14 Combine like terms: 14 + -14 = 0 0 + m = -12.529964086 + -14 m = -12.529964086 + -14 Combine like terms: -12.529964086 + -14 = -26.529964086 m = -26.529964086 Simplifying m = -26.529964086Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.470035914, -26.529964086}
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