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Simplifying m2 + -6m + -6 = 0 Reorder the terms: -6 + -6m + m2 = 0 Solving -6 + -6m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -6m + 6 + m2 = 0 + 6 Reorder the terms: -6 + 6 + -6m + m2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6m + m2 = 0 + 6 -6m + m2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6m + m2 = 6 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 = 6 + 9 Reorder the terms: 9 + -6m + m2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + -6m + m2 = 15 Factor a perfect square on the left side: (m + -3)(m + -3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (m + -3) equal to 3.872983346 and -3.872983346.Subproblem 1
m + -3 = 3.872983346 Simplifying m + -3 = 3.872983346 Reorder the terms: -3 + m = 3.872983346 Solving -3 + m = 3.872983346 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 = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + m = 3.872983346 + 3 m = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 m = 6.872983346 Simplifying m = 6.872983346Subproblem 2
m + -3 = -3.872983346 Simplifying m + -3 = -3.872983346 Reorder the terms: -3 + m = -3.872983346 Solving -3 + m = -3.872983346 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 = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + m = -3.872983346 + 3 m = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 m = -0.872983346 Simplifying m = -0.872983346Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.872983346, -0.872983346}
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