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Simplifying m2 + -6m + -18 = 0 Reorder the terms: -18 + -6m + m2 = 0 Solving -18 + -6m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6m + 18 + m2 = 0 + 18 Reorder the terms: -18 + 18 + -6m + m2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6m + m2 = 0 + 18 -6m + m2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6m + m2 = 18 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 = 18 + 9 Reorder the terms: 9 + -6m + m2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6m + m2 = 27 Factor a perfect square on the left side: (m + -3)(m + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (m + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
m + -3 = 5.196152423 Simplifying m + -3 = 5.196152423 Reorder the terms: -3 + m = 5.196152423 Solving -3 + m = 5.196152423 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 = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + m = 5.196152423 + 3 m = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 m = 8.196152423 Simplifying m = 8.196152423Subproblem 2
m + -3 = -5.196152423 Simplifying m + -3 = -5.196152423 Reorder the terms: -3 + m = -5.196152423 Solving -3 + m = -5.196152423 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 = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + m = -5.196152423 + 3 m = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 m = -2.196152423 Simplifying m = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.196152423, -2.196152423}
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