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Simplifying m2 + 8m + -2 = 0 Reorder the terms: -2 + 8m + m2 = 0 Solving -2 + 8m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 8m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + 8m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 8m + m2 = 0 + 2 8m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 8m + m2 = 2 The m term is 8m. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8m + 16 + m2 = 2 + 16 Reorder the terms: 16 + 8m + m2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + 8m + m2 = 18 Factor a perfect square on the left side: (m + 4)(m + 4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (m + 4) equal to 4.242640687 and -4.242640687.Subproblem 1
m + 4 = 4.242640687 Simplifying m + 4 = 4.242640687 Reorder the terms: 4 + m = 4.242640687 Solving 4 + m = 4.242640687 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = 4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + m = 4.242640687 + -4 m = 4.242640687 + -4 Combine like terms: 4.242640687 + -4 = 0.242640687 m = 0.242640687 Simplifying m = 0.242640687Subproblem 2
m + 4 = -4.242640687 Simplifying m + 4 = -4.242640687 Reorder the terms: 4 + m = -4.242640687 Solving 4 + m = -4.242640687 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = -4.242640687 + -4 Combine like terms: 4 + -4 = 0 0 + m = -4.242640687 + -4 m = -4.242640687 + -4 Combine like terms: -4.242640687 + -4 = -8.242640687 m = -8.242640687 Simplifying m = -8.242640687Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.242640687, -8.242640687}
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