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Simplifying m2 + -13m + 21 = 0 Reorder the terms: 21 + -13m + m2 = 0 Solving 21 + -13m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -13m + -21 + m2 = 0 + -21 Reorder the terms: 21 + -21 + -13m + m2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -13m + m2 = 0 + -21 -13m + m2 = 0 + -21 Combine like terms: 0 + -21 = -21 -13m + m2 = -21 The m term is -13m. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13m + 42.25 + m2 = -21 + 42.25 Reorder the terms: 42.25 + -13m + m2 = -21 + 42.25 Combine like terms: -21 + 42.25 = 21.25 42.25 + -13m + m2 = 21.25 Factor a perfect square on the left side: (m + -6.5)(m + -6.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (m + -6.5) equal to 4.609772229 and -4.609772229.Subproblem 1
m + -6.5 = 4.609772229 Simplifying m + -6.5 = 4.609772229 Reorder the terms: -6.5 + m = 4.609772229 Solving -6.5 + m = 4.609772229 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + m = 4.609772229 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + m = 4.609772229 + 6.5 m = 4.609772229 + 6.5 Combine like terms: 4.609772229 + 6.5 = 11.109772229 m = 11.109772229 Simplifying m = 11.109772229Subproblem 2
m + -6.5 = -4.609772229 Simplifying m + -6.5 = -4.609772229 Reorder the terms: -6.5 + m = -4.609772229 Solving -6.5 + m = -4.609772229 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + m = -4.609772229 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + m = -4.609772229 + 6.5 m = -4.609772229 + 6.5 Combine like terms: -4.609772229 + 6.5 = 1.890227771 m = 1.890227771 Simplifying m = 1.890227771Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.109772229, 1.890227771}
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