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Simplifying m2 = 11(m + -2) Reorder the terms: m2 = 11(-2 + m) m2 = (-2 * 11 + m * 11) m2 = (-22 + 11m) Solving m2 = -22 + 11m Solving for variable 'm'. Reorder the terms: 22 + -11m + m2 = -22 + 11m + 22 + -11m Reorder the terms: 22 + -11m + m2 = -22 + 22 + 11m + -11m Combine like terms: -22 + 22 = 0 22 + -11m + m2 = 0 + 11m + -11m 22 + -11m + m2 = 11m + -11m Combine like terms: 11m + -11m = 0 22 + -11m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + -11m + -22 + m2 = 0 + -22 Reorder the terms: 22 + -22 + -11m + m2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -11m + m2 = 0 + -22 -11m + m2 = 0 + -22 Combine like terms: 0 + -22 = -22 -11m + m2 = -22 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 = -22 + 30.25 Reorder the terms: 30.25 + -11m + m2 = -22 + 30.25 Combine like terms: -22 + 30.25 = 8.25 30.25 + -11m + m2 = 8.25 Factor a perfect square on the left side: (m + -5.5)(m + -5.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (m + -5.5) equal to 2.872281323 and -2.872281323.Subproblem 1
m + -5.5 = 2.872281323 Simplifying m + -5.5 = 2.872281323 Reorder the terms: -5.5 + m = 2.872281323 Solving -5.5 + m = 2.872281323 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 = 2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = 2.872281323 + 5.5 m = 2.872281323 + 5.5 Combine like terms: 2.872281323 + 5.5 = 8.372281323 m = 8.372281323 Simplifying m = 8.372281323Subproblem 2
m + -5.5 = -2.872281323 Simplifying m + -5.5 = -2.872281323 Reorder the terms: -5.5 + m = -2.872281323 Solving -5.5 + m = -2.872281323 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 = -2.872281323 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = -2.872281323 + 5.5 m = -2.872281323 + 5.5 Combine like terms: -2.872281323 + 5.5 = 2.627718677 m = 2.627718677 Simplifying m = 2.627718677Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.372281323, 2.627718677}
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