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Simplifying m2 + -8m + -23 = 0 Reorder the terms: -23 + -8m + m2 = 0 Solving -23 + -8m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -8m + 23 + m2 = 0 + 23 Reorder the terms: -23 + 23 + -8m + m2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -8m + m2 = 0 + 23 -8m + m2 = 0 + 23 Combine like terms: 0 + 23 = 23 -8m + m2 = 23 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 = 23 + 16 Reorder the terms: 16 + -8m + m2 = 23 + 16 Combine like terms: 23 + 16 = 39 16 + -8m + m2 = 39 Factor a perfect square on the left side: (m + -4)(m + -4) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (m + -4) equal to 6.244997998 and -6.244997998.Subproblem 1
m + -4 = 6.244997998 Simplifying m + -4 = 6.244997998 Reorder the terms: -4 + m = 6.244997998 Solving -4 + m = 6.244997998 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 = 6.244997998 + 4 Combine like terms: -4 + 4 = 0 0 + m = 6.244997998 + 4 m = 6.244997998 + 4 Combine like terms: 6.244997998 + 4 = 10.244997998 m = 10.244997998 Simplifying m = 10.244997998Subproblem 2
m + -4 = -6.244997998 Simplifying m + -4 = -6.244997998 Reorder the terms: -4 + m = -6.244997998 Solving -4 + m = -6.244997998 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 = -6.244997998 + 4 Combine like terms: -4 + 4 = 0 0 + m = -6.244997998 + 4 m = -6.244997998 + 4 Combine like terms: -6.244997998 + 4 = -2.244997998 m = -2.244997998 Simplifying m = -2.244997998Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.244997998, -2.244997998}
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