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Simplifying m2 + 2m + -14 = 0 Reorder the terms: -14 + 2m + m2 = 0 Solving -14 + 2m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 2m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + 2m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2m + m2 = 0 + 14 2m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 2m + m2 = 14 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 14 + 1 Reorder the terms: 1 + 2m + m2 = 14 + 1 Combine like terms: 14 + 1 = 15 1 + 2m + m2 = 15 Factor a perfect square on the left side: (m + 1)(m + 1) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (m + 1) equal to 3.872983346 and -3.872983346.Subproblem 1
m + 1 = 3.872983346 Simplifying m + 1 = 3.872983346 Reorder the terms: 1 + m = 3.872983346 Solving 1 + m = 3.872983346 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + m = 3.872983346 + -1 m = 3.872983346 + -1 Combine like terms: 3.872983346 + -1 = 2.872983346 m = 2.872983346 Simplifying m = 2.872983346Subproblem 2
m + 1 = -3.872983346 Simplifying m + 1 = -3.872983346 Reorder the terms: 1 + m = -3.872983346 Solving 1 + m = -3.872983346 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -3.872983346 + -1 Combine like terms: 1 + -1 = 0 0 + m = -3.872983346 + -1 m = -3.872983346 + -1 Combine like terms: -3.872983346 + -1 = -4.872983346 m = -4.872983346 Simplifying m = -4.872983346Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.872983346, -4.872983346}
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