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Simplifying 6m2 + 66m + 121 = 0 Reorder the terms: 121 + 66m + 6m2 = 0 Solving 121 + 66m + 6m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 20.16666667 + 11m + m2 = 0 Move the constant term to the right: Add '-20.16666667' to each side of the equation. 20.16666667 + 11m + -20.16666667 + m2 = 0 + -20.16666667 Reorder the terms: 20.16666667 + -20.16666667 + 11m + m2 = 0 + -20.16666667 Combine like terms: 20.16666667 + -20.16666667 = 0.00000000 0.00000000 + 11m + m2 = 0 + -20.16666667 11m + m2 = 0 + -20.16666667 Combine like terms: 0 + -20.16666667 = -20.16666667 11m + m2 = -20.16666667 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 = -20.16666667 + 30.25 Reorder the terms: 30.25 + 11m + m2 = -20.16666667 + 30.25 Combine like terms: -20.16666667 + 30.25 = 10.08333333 30.25 + 11m + m2 = 10.08333333 Factor a perfect square on the left side: (m + 5.5)(m + 5.5) = 10.08333333 Calculate the square root of the right side: 3.17542648 Break this problem into two subproblems by setting (m + 5.5) equal to 3.17542648 and -3.17542648.Subproblem 1
m + 5.5 = 3.17542648 Simplifying m + 5.5 = 3.17542648 Reorder the terms: 5.5 + m = 3.17542648 Solving 5.5 + m = 3.17542648 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 = 3.17542648 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = 3.17542648 + -5.5 m = 3.17542648 + -5.5 Combine like terms: 3.17542648 + -5.5 = -2.32457352 m = -2.32457352 Simplifying m = -2.32457352Subproblem 2
m + 5.5 = -3.17542648 Simplifying m + 5.5 = -3.17542648 Reorder the terms: 5.5 + m = -3.17542648 Solving 5.5 + m = -3.17542648 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 = -3.17542648 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + m = -3.17542648 + -5.5 m = -3.17542648 + -5.5 Combine like terms: -3.17542648 + -5.5 = -8.67542648 m = -8.67542648 Simplifying m = -8.67542648Solution
The solution to the problem is based on the solutions from the subproblems. m = {-2.32457352, -8.67542648}
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