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Simplifying 11m2 + 11m = 8 Reorder the terms: 11m + 11m2 = 8 Solving 11m + 11m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + 11m + 11m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 11m + 11m2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + m + m2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + m + 0.7272727273 + m2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + m + m2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + m + m2 = 0 + 0.7272727273 m + m2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 m + m2 = 0.7272727273 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = 0.7272727273 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 0.7272727273 + 0.25 Combine like terms: 0.7272727273 + 0.25 = 0.9772727273 1.25 + m2 = 0.9772727273 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 0.9772727273 Calculate the square root of the right side: 0.988571053 Break this problem into two subproblems by setting (m + 0.5) equal to 0.988571053 and -0.988571053.Subproblem 1
m + 0.5 = 0.988571053 Simplifying m + 0.5 = 0.988571053 Reorder the terms: 0.5 + m = 0.988571053 Solving 0.5 + m = 0.988571053 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 0.988571053 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 0.988571053 + -0.5 m = 0.988571053 + -0.5 Combine like terms: 0.988571053 + -0.5 = 0.488571053 m = 0.488571053 Simplifying m = 0.488571053Subproblem 2
m + 0.5 = -0.988571053 Simplifying m + 0.5 = -0.988571053 Reorder the terms: 0.5 + m = -0.988571053 Solving 0.5 + m = -0.988571053 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -0.988571053 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -0.988571053 + -0.5 m = -0.988571053 + -0.5 Combine like terms: -0.988571053 + -0.5 = -1.488571053 m = -1.488571053 Simplifying m = -1.488571053Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.488571053, -1.488571053}
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