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Simplifying m2 + 11m + 5 = 0 Reorder the terms: 5 + 11m + m2 = 0 Solving 5 + 11m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 11m + -5 + m2 = 0 + -5 Reorder the terms: 5 + -5 + 11m + m2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 11m + m2 = 0 + -5 11m + m2 = 0 + -5 Combine like terms: 0 + -5 = -5 11m + m2 = -5 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 = -5 + 30.25 Reorder the terms: 30.25 + 11m + m2 = -5 + 30.25 Combine like terms: -5 + 30.25 = 25.25 30.25 + 11m + m2 = 25.25 Factor a perfect square on the left side: (m + 5.5)(m + 5.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (m + 5.5) equal to 5.024937811 and -5.024937811.Subproblem 1
m + 5.5 = 5.024937811 Simplifying m + 5.5 = 5.024937811 Reorder the terms: 5.5 + m = 5.024937811 Solving 5.5 + m = 5.024937811 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 = 5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = 5.024937811 + -5.5 m = 5.024937811 + -5.5 Combine like terms: 5.024937811 + -5.5 = -0.475062189 m = -0.475062189 Simplifying m = -0.475062189Subproblem 2
m + 5.5 = -5.024937811 Simplifying m + 5.5 = -5.024937811 Reorder the terms: 5.5 + m = -5.024937811 Solving 5.5 + m = -5.024937811 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 = -5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = -5.024937811 + -5.5 m = -5.024937811 + -5.5 Combine like terms: -5.024937811 + -5.5 = -10.524937811 m = -10.524937811 Simplifying m = -10.524937811Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.475062189, -10.524937811}
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