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Simplifying m2 + -6m + -121 = 0 Reorder the terms: -121 + -6m + m2 = 0 Solving -121 + -6m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + -6m + 121 + m2 = 0 + 121 Reorder the terms: -121 + 121 + -6m + m2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + -6m + m2 = 0 + 121 -6m + m2 = 0 + 121 Combine like terms: 0 + 121 = 121 -6m + m2 = 121 The m term is -6m. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6m + 9 + m2 = 121 + 9 Reorder the terms: 9 + -6m + m2 = 121 + 9 Combine like terms: 121 + 9 = 130 9 + -6m + m2 = 130 Factor a perfect square on the left side: (m + -3)(m + -3) = 130 Calculate the square root of the right side: 11.401754251 Break this problem into two subproblems by setting (m + -3) equal to 11.401754251 and -11.401754251.Subproblem 1
m + -3 = 11.401754251 Simplifying m + -3 = 11.401754251 Reorder the terms: -3 + m = 11.401754251 Solving -3 + m = 11.401754251 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 11.401754251 + 3 Combine like terms: -3 + 3 = 0 0 + m = 11.401754251 + 3 m = 11.401754251 + 3 Combine like terms: 11.401754251 + 3 = 14.401754251 m = 14.401754251 Simplifying m = 14.401754251Subproblem 2
m + -3 = -11.401754251 Simplifying m + -3 = -11.401754251 Reorder the terms: -3 + m = -11.401754251 Solving -3 + m = -11.401754251 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -11.401754251 + 3 Combine like terms: -3 + 3 = 0 0 + m = -11.401754251 + 3 m = -11.401754251 + 3 Combine like terms: -11.401754251 + 3 = -8.401754251 m = -8.401754251 Simplifying m = -8.401754251Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.401754251, -8.401754251}
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