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Simplifying 11m2 + -10m + 2 = 9 Reorder the terms: 2 + -10m + 11m2 = 9 Solving 2 + -10m + 11m2 = 9 Solving for variable 'm'. Reorder the terms: 2 + -9 + -10m + 11m2 = 9 + -9 Combine like terms: 2 + -9 = -7 -7 + -10m + 11m2 = 9 + -9 Combine like terms: 9 + -9 = 0 -7 + -10m + 11m2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.6363636364 + -0.9090909091m + m2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + -0.9090909091m + 0.6363636364 + m2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + -0.9090909091m + m2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + -0.9090909091m + m2 = 0 + 0.6363636364 -0.9090909091m + m2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 -0.9090909091m + m2 = 0.6363636364 The m term is -0.9090909091m. Take half its coefficient (-0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. -0.9090909091m + 0.2066115703 + m2 = 0.6363636364 + 0.2066115703 Reorder the terms: 0.2066115703 + -0.9090909091m + m2 = 0.6363636364 + 0.2066115703 Combine like terms: 0.6363636364 + 0.2066115703 = 0.8429752067 0.2066115703 + -0.9090909091m + m2 = 0.8429752067 Factor a perfect square on the left side: (m + -0.4545454546)(m + -0.4545454546) = 0.8429752067 Calculate the square root of the right side: 0.918136813 Break this problem into two subproblems by setting (m + -0.4545454546) equal to 0.918136813 and -0.918136813.Subproblem 1
m + -0.4545454546 = 0.918136813 Simplifying m + -0.4545454546 = 0.918136813 Reorder the terms: -0.4545454546 + m = 0.918136813 Solving -0.4545454546 + m = 0.918136813 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + m = 0.918136813 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + m = 0.918136813 + 0.4545454546 m = 0.918136813 + 0.4545454546 Combine like terms: 0.918136813 + 0.4545454546 = 1.3726822676 m = 1.3726822676 Simplifying m = 1.3726822676Subproblem 2
m + -0.4545454546 = -0.918136813 Simplifying m + -0.4545454546 = -0.918136813 Reorder the terms: -0.4545454546 + m = -0.918136813 Solving -0.4545454546 + m = -0.918136813 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + m = -0.918136813 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + m = -0.918136813 + 0.4545454546 m = -0.918136813 + 0.4545454546 Combine like terms: -0.918136813 + 0.4545454546 = -0.4635913584 m = -0.4635913584 Simplifying m = -0.4635913584Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.3726822676, -0.4635913584}
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