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Simplifying (m + -6)(m + 7) = 2 Reorder the terms: (-6 + m)(m + 7) = 2 Reorder the terms: (-6 + m)(7 + m) = 2 Multiply (-6 + m) * (7 + m) (-6(7 + m) + m(7 + m)) = 2 ((7 * -6 + m * -6) + m(7 + m)) = 2 ((-42 + -6m) + m(7 + m)) = 2 (-42 + -6m + (7 * m + m * m)) = 2 (-42 + -6m + (7m + m2)) = 2 Combine like terms: -6m + 7m = 1m (-42 + 1m + m2) = 2 Solving -42 + 1m + m2 = 2 Solving for variable 'm'. Reorder the terms: -42 + -2 + 1m + m2 = 2 + -2 Combine like terms: -42 + -2 = -44 -44 + 1m + m2 = 2 + -2 Combine like terms: 2 + -2 = 0 -44 + 1m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 1m + 44 + m2 = 0 + 44 Reorder the terms: -44 + 44 + 1m + m2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 1m + m2 = 0 + 44 1m + m2 = 0 + 44 Combine like terms: 0 + 44 = 44 1m + m2 = 44 The m term is 1m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. m + 0.25 + m2 = 44 + 0.25 Reorder the terms: 0.25 + m + m2 = 44 + 0.25 Combine like terms: 44 + 0.25 = 44.25 0.25 + m + m2 = 44.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (m + 0.5) equal to 6.652067348 and -6.652067348.Subproblem 1
m + 0.5 = 6.652067348 Simplifying m + 0.5 = 6.652067348 Reorder the terms: 0.5 + m = 6.652067348 Solving 0.5 + m = 6.652067348 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 6.652067348 + -0.5 m = 6.652067348 + -0.5 Combine like terms: 6.652067348 + -0.5 = 6.152067348 m = 6.152067348 Simplifying m = 6.152067348Subproblem 2
m + 0.5 = -6.652067348 Simplifying m + 0.5 = -6.652067348 Reorder the terms: 0.5 + m = -6.652067348 Solving 0.5 + m = -6.652067348 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -6.652067348 + -0.5 m = -6.652067348 + -0.5 Combine like terms: -6.652067348 + -0.5 = -7.152067348 m = -7.152067348 Simplifying m = -7.152067348Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.152067348, -7.152067348}
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