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Simplifying 11m2 + -11m + -1 = 9m Reorder the terms: -1 + -11m + 11m2 = 9m Solving -1 + -11m + 11m2 = 9m Solving for variable 'm'. Reorder the terms: -1 + -11m + -9m + 11m2 = 9m + -9m Combine like terms: -11m + -9m = -20m -1 + -20m + 11m2 = 9m + -9m Combine like terms: 9m + -9m = 0 -1 + -20m + 11m2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.09090909091 + -1.818181818m + m2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + -1.818181818m + 0.09090909091 + m2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + -1.818181818m + m2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + -1.818181818m + m2 = 0 + 0.09090909091 -1.818181818m + m2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 -1.818181818m + m2 = 0.09090909091 The m term is -1.818181818m. Take half its coefficient (-0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. -1.818181818m + 0.8264462808 + m2 = 0.09090909091 + 0.8264462808 Reorder the terms: 0.8264462808 + -1.818181818m + m2 = 0.09090909091 + 0.8264462808 Combine like terms: 0.09090909091 + 0.8264462808 = 0.91735537171 0.8264462808 + -1.818181818m + m2 = 0.91735537171 Factor a perfect square on the left side: (m + -0.909090909)(m + -0.909090909) = 0.91735537171 Calculate the square root of the right side: 0.957786705 Break this problem into two subproblems by setting (m + -0.909090909) equal to 0.957786705 and -0.957786705.Subproblem 1
m + -0.909090909 = 0.957786705 Simplifying m + -0.909090909 = 0.957786705 Reorder the terms: -0.909090909 + m = 0.957786705 Solving -0.909090909 + m = 0.957786705 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + m = 0.957786705 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + m = 0.957786705 + 0.909090909 m = 0.957786705 + 0.909090909 Combine like terms: 0.957786705 + 0.909090909 = 1.866877614 m = 1.866877614 Simplifying m = 1.866877614Subproblem 2
m + -0.909090909 = -0.957786705 Simplifying m + -0.909090909 = -0.957786705 Reorder the terms: -0.909090909 + m = -0.957786705 Solving -0.909090909 + m = -0.957786705 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + m = -0.957786705 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + m = -0.957786705 + 0.909090909 m = -0.957786705 + 0.909090909 Combine like terms: -0.957786705 + 0.909090909 = -0.048695796 m = -0.048695796 Simplifying m = -0.048695796Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.866877614, -0.048695796}
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