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Simplifying m2 + 26m + -37 = 0 Reorder the terms: -37 + 26m + m2 = 0 Solving -37 + 26m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 26m + 37 + m2 = 0 + 37 Reorder the terms: -37 + 37 + 26m + m2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 26m + m2 = 0 + 37 26m + m2 = 0 + 37 Combine like terms: 0 + 37 = 37 26m + m2 = 37 The m term is 26m. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26m + 169 + m2 = 37 + 169 Reorder the terms: 169 + 26m + m2 = 37 + 169 Combine like terms: 37 + 169 = 206 169 + 26m + m2 = 206 Factor a perfect square on the left side: (m + 13)(m + 13) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting (m + 13) equal to 14.352700094 and -14.352700094.Subproblem 1
m + 13 = 14.352700094 Simplifying m + 13 = 14.352700094 Reorder the terms: 13 + m = 14.352700094 Solving 13 + m = 14.352700094 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + m = 14.352700094 + -13 Combine like terms: 13 + -13 = 0 0 + m = 14.352700094 + -13 m = 14.352700094 + -13 Combine like terms: 14.352700094 + -13 = 1.352700094 m = 1.352700094 Simplifying m = 1.352700094Subproblem 2
m + 13 = -14.352700094 Simplifying m + 13 = -14.352700094 Reorder the terms: 13 + m = -14.352700094 Solving 13 + m = -14.352700094 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + m = -14.352700094 + -13 Combine like terms: 13 + -13 = 0 0 + m = -14.352700094 + -13 m = -14.352700094 + -13 Combine like terms: -14.352700094 + -13 = -27.352700094 m = -27.352700094 Simplifying m = -27.352700094Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.352700094, -27.352700094}
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