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Simplifying m2 + 2m + -13 = 0 Reorder the terms: -13 + 2m + m2 = 0 Solving -13 + 2m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 2m + 13 + m2 = 0 + 13 Reorder the terms: -13 + 13 + 2m + m2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 2m + m2 = 0 + 13 2m + m2 = 0 + 13 Combine like terms: 0 + 13 = 13 2m + m2 = 13 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 = 13 + 1 Reorder the terms: 1 + 2m + m2 = 13 + 1 Combine like terms: 13 + 1 = 14 1 + 2m + m2 = 14 Factor a perfect square on the left side: (m + 1)(m + 1) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (m + 1) equal to 3.741657387 and -3.741657387.Subproblem 1
m + 1 = 3.741657387 Simplifying m + 1 = 3.741657387 Reorder the terms: 1 + m = 3.741657387 Solving 1 + m = 3.741657387 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 = 3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + m = 3.741657387 + -1 m = 3.741657387 + -1 Combine like terms: 3.741657387 + -1 = 2.741657387 m = 2.741657387 Simplifying m = 2.741657387Subproblem 2
m + 1 = -3.741657387 Simplifying m + 1 = -3.741657387 Reorder the terms: 1 + m = -3.741657387 Solving 1 + m = -3.741657387 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 = -3.741657387 + -1 Combine like terms: 1 + -1 = 0 0 + m = -3.741657387 + -1 m = -3.741657387 + -1 Combine like terms: -3.741657387 + -1 = -4.741657387 m = -4.741657387 Simplifying m = -4.741657387Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.741657387, -4.741657387}
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