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Simplifying m2 + 11m + 1 = 0 Reorder the terms: 1 + 11m + m2 = 0 Solving 1 + 11m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 11m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + 11m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 11m + m2 = 0 + -1 11m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 11m + m2 = -1 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 = -1 + 30.25 Reorder the terms: 30.25 + 11m + m2 = -1 + 30.25 Combine like terms: -1 + 30.25 = 29.25 30.25 + 11m + m2 = 29.25 Factor a perfect square on the left side: (m + 5.5)(m + 5.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (m + 5.5) equal to 5.408326913 and -5.408326913.Subproblem 1
m + 5.5 = 5.408326913 Simplifying m + 5.5 = 5.408326913 Reorder the terms: 5.5 + m = 5.408326913 Solving 5.5 + m = 5.408326913 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 = 5.408326913 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = 5.408326913 + -5.5 m = 5.408326913 + -5.5 Combine like terms: 5.408326913 + -5.5 = -0.091673087 m = -0.091673087 Simplifying m = -0.091673087Subproblem 2
m + 5.5 = -5.408326913 Simplifying m + 5.5 = -5.408326913 Reorder the terms: 5.5 + m = -5.408326913 Solving 5.5 + m = -5.408326913 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 = -5.408326913 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = -5.408326913 + -5.5 m = -5.408326913 + -5.5 Combine like terms: -5.408326913 + -5.5 = -10.908326913 m = -10.908326913 Simplifying m = -10.908326913Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.091673087, -10.908326913}
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