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Simplifying m2 + 23m + 24 = 0 Reorder the terms: 24 + 23m + m2 = 0 Solving 24 + 23m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 23m + -24 + m2 = 0 + -24 Reorder the terms: 24 + -24 + 23m + m2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 23m + m2 = 0 + -24 23m + m2 = 0 + -24 Combine like terms: 0 + -24 = -24 23m + m2 = -24 The m term is 23m. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23m + 132.25 + m2 = -24 + 132.25 Reorder the terms: 132.25 + 23m + m2 = -24 + 132.25 Combine like terms: -24 + 132.25 = 108.25 132.25 + 23m + m2 = 108.25 Factor a perfect square on the left side: (m + 11.5)(m + 11.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (m + 11.5) equal to 10.404326023 and -10.404326023.Subproblem 1
m + 11.5 = 10.404326023 Simplifying m + 11.5 = 10.404326023 Reorder the terms: 11.5 + m = 10.404326023 Solving 11.5 + m = 10.404326023 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + m = 10.404326023 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + m = 10.404326023 + -11.5 m = 10.404326023 + -11.5 Combine like terms: 10.404326023 + -11.5 = -1.095673977 m = -1.095673977 Simplifying m = -1.095673977Subproblem 2
m + 11.5 = -10.404326023 Simplifying m + 11.5 = -10.404326023 Reorder the terms: 11.5 + m = -10.404326023 Solving 11.5 + m = -10.404326023 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + m = -10.404326023 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + m = -10.404326023 + -11.5 m = -10.404326023 + -11.5 Combine like terms: -10.404326023 + -11.5 = -21.904326023 m = -21.904326023 Simplifying m = -21.904326023Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.095673977, -21.904326023}
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