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Simplifying m2 + 11m = 24 Reorder the terms: 11m + m2 = 24 Solving 11m + m2 = 24 Solving for variable 'm'. Reorder the terms: -24 + 11m + m2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 11m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 11m + 24 + m2 = 0 + 24 Reorder the terms: -24 + 24 + 11m + m2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 11m + m2 = 0 + 24 11m + m2 = 0 + 24 Combine like terms: 0 + 24 = 24 11m + m2 = 24 The m term is 11m. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11m + 30.25 + m2 = 24 + 30.25 Reorder the terms: 30.25 + 11m + m2 = 24 + 30.25 Combine like terms: 24 + 30.25 = 54.25 30.25 + 11m + m2 = 54.25 Factor a perfect square on the left side: (m + 5.5)(m + 5.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (m + 5.5) equal to 7.365459931 and -7.365459931.Subproblem 1
m + 5.5 = 7.365459931 Simplifying m + 5.5 = 7.365459931 Reorder the terms: 5.5 + m = 7.365459931 Solving 5.5 + m = 7.365459931 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + m = 7.365459931 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = 7.365459931 + -5.5 m = 7.365459931 + -5.5 Combine like terms: 7.365459931 + -5.5 = 1.865459931 m = 1.865459931 Simplifying m = 1.865459931Subproblem 2
m + 5.5 = -7.365459931 Simplifying m + 5.5 = -7.365459931 Reorder the terms: 5.5 + m = -7.365459931 Solving 5.5 + m = -7.365459931 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + m = -7.365459931 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = -7.365459931 + -5.5 m = -7.365459931 + -5.5 Combine like terms: -7.365459931 + -5.5 = -12.865459931 m = -12.865459931 Simplifying m = -12.865459931Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.865459931, -12.865459931}
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