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Simplifying m2 + 22m + 24 = 0 Reorder the terms: 24 + 22m + m2 = 0 Solving 24 + 22m + 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 + 22m + -24 + m2 = 0 + -24 Reorder the terms: 24 + -24 + 22m + m2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 22m + m2 = 0 + -24 22m + m2 = 0 + -24 Combine like terms: 0 + -24 = -24 22m + m2 = -24 The m term is 22m. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22m + 121 + m2 = -24 + 121 Reorder the terms: 121 + 22m + m2 = -24 + 121 Combine like terms: -24 + 121 = 97 121 + 22m + m2 = 97 Factor a perfect square on the left side: (m + 11)(m + 11) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (m + 11) equal to 9.848857802 and -9.848857802.Subproblem 1
m + 11 = 9.848857802 Simplifying m + 11 = 9.848857802 Reorder the terms: 11 + m = 9.848857802 Solving 11 + m = 9.848857802 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + m = 9.848857802 + -11 Combine like terms: 11 + -11 = 0 0 + m = 9.848857802 + -11 m = 9.848857802 + -11 Combine like terms: 9.848857802 + -11 = -1.151142198 m = -1.151142198 Simplifying m = -1.151142198Subproblem 2
m + 11 = -9.848857802 Simplifying m + 11 = -9.848857802 Reorder the terms: 11 + m = -9.848857802 Solving 11 + m = -9.848857802 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + m = -9.848857802 + -11 Combine like terms: 11 + -11 = 0 0 + m = -9.848857802 + -11 m = -9.848857802 + -11 Combine like terms: -9.848857802 + -11 = -20.848857802 m = -20.848857802 Simplifying m = -20.848857802Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.151142198, -20.848857802}
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