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Simplifying (m + -5)(m + -5) = 13 Reorder the terms: (-5 + m)(m + -5) = 13 Reorder the terms: (-5 + m)(-5 + m) = 13 Multiply (-5 + m) * (-5 + m) (-5(-5 + m) + m(-5 + m)) = 13 ((-5 * -5 + m * -5) + m(-5 + m)) = 13 ((25 + -5m) + m(-5 + m)) = 13 (25 + -5m + (-5 * m + m * m)) = 13 (25 + -5m + (-5m + m2)) = 13 Combine like terms: -5m + -5m = -10m (25 + -10m + m2) = 13 Solving 25 + -10m + m2 = 13 Solving for variable 'm'. Reorder the terms: 25 + -13 + -10m + m2 = 13 + -13 Combine like terms: 25 + -13 = 12 12 + -10m + m2 = 13 + -13 Combine like terms: 13 + -13 = 0 12 + -10m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -10m + -12 + m2 = 0 + -12 Reorder the terms: 12 + -12 + -10m + m2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -10m + m2 = 0 + -12 -10m + m2 = 0 + -12 Combine like terms: 0 + -12 = -12 -10m + m2 = -12 The m term is -10m. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10m + 25 + m2 = -12 + 25 Reorder the terms: 25 + -10m + m2 = -12 + 25 Combine like terms: -12 + 25 = 13 25 + -10m + m2 = 13 Factor a perfect square on the left side: (m + -5)(m + -5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (m + -5) equal to 3.605551275 and -3.605551275.Subproblem 1
m + -5 = 3.605551275 Simplifying m + -5 = 3.605551275 Reorder the terms: -5 + m = 3.605551275 Solving -5 + m = 3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = 3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + m = 3.605551275 + 5 m = 3.605551275 + 5 Combine like terms: 3.605551275 + 5 = 8.605551275 m = 8.605551275 Simplifying m = 8.605551275Subproblem 2
m + -5 = -3.605551275 Simplifying m + -5 = -3.605551275 Reorder the terms: -5 + m = -3.605551275 Solving -5 + m = -3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + m = -3.605551275 + 5 Combine like terms: -5 + 5 = 0 0 + m = -3.605551275 + 5 m = -3.605551275 + 5 Combine like terms: -3.605551275 + 5 = 1.394448725 m = 1.394448725 Simplifying m = 1.394448725Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.605551275, 1.394448725}
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