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Simplifying 8 = 11m + -1m * m Multiply m * m 8 = 11m + -1m2 Solving 8 = 11m + -1m2 Solving for variable 'm'. Reorder the terms: 8 + -11m + m2 = 11m + -11m + -1m2 + m2 Combine like terms: 11m + -11m = 0 8 + -11m + m2 = 0 + -1m2 + m2 8 + -11m + m2 = -1m2 + m2 Combine like terms: -1m2 + m2 = 0 8 + -11m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -11m + -8 + m2 = 0 + -8 Reorder the terms: 8 + -8 + -11m + m2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -11m + m2 = 0 + -8 -11m + m2 = 0 + -8 Combine like terms: 0 + -8 = -8 -11m + m2 = -8 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 = -8 + 30.25 Reorder the terms: 30.25 + -11m + m2 = -8 + 30.25 Combine like terms: -8 + 30.25 = 22.25 30.25 + -11m + m2 = 22.25 Factor a perfect square on the left side: (m + -5.5)(m + -5.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (m + -5.5) equal to 4.716990566 and -4.716990566.Subproblem 1
m + -5.5 = 4.716990566 Simplifying m + -5.5 = 4.716990566 Reorder the terms: -5.5 + m = 4.716990566 Solving -5.5 + m = 4.716990566 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 = 4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = 4.716990566 + 5.5 m = 4.716990566 + 5.5 Combine like terms: 4.716990566 + 5.5 = 10.216990566 m = 10.216990566 Simplifying m = 10.216990566Subproblem 2
m + -5.5 = -4.716990566 Simplifying m + -5.5 = -4.716990566 Reorder the terms: -5.5 + m = -4.716990566 Solving -5.5 + m = -4.716990566 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 = -4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = -4.716990566 + 5.5 m = -4.716990566 + 5.5 Combine like terms: -4.716990566 + 5.5 = 0.783009434 m = 0.783009434 Simplifying m = 0.783009434Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.216990566, 0.783009434}
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