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Simplifying (r + -2)(r + 10) = 12 Reorder the terms: (-2 + r)(r + 10) = 12 Reorder the terms: (-2 + r)(10 + r) = 12 Multiply (-2 + r) * (10 + r) (-2(10 + r) + r(10 + r)) = 12 ((10 * -2 + r * -2) + r(10 + r)) = 12 ((-20 + -2r) + r(10 + r)) = 12 (-20 + -2r + (10 * r + r * r)) = 12 (-20 + -2r + (10r + r2)) = 12 Combine like terms: -2r + 10r = 8r (-20 + 8r + r2) = 12 Solving -20 + 8r + r2 = 12 Solving for variable 'r'. Reorder the terms: -20 + -12 + 8r + r2 = 12 + -12 Combine like terms: -20 + -12 = -32 -32 + 8r + r2 = 12 + -12 Combine like terms: 12 + -12 = 0 -32 + 8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 8r + 32 + r2 = 0 + 32 Reorder the terms: -32 + 32 + 8r + r2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 8r + r2 = 0 + 32 8r + r2 = 0 + 32 Combine like terms: 0 + 32 = 32 8r + r2 = 32 The r term is 8r. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8r + 16 + r2 = 32 + 16 Reorder the terms: 16 + 8r + r2 = 32 + 16 Combine like terms: 32 + 16 = 48 16 + 8r + r2 = 48 Factor a perfect square on the left side: (r + 4)(r + 4) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (r + 4) equal to 6.92820323 and -6.92820323.Subproblem 1
r + 4 = 6.92820323 Simplifying r + 4 = 6.92820323 Reorder the terms: 4 + r = 6.92820323 Solving 4 + r = 6.92820323 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 6.92820323 + -4 Combine like terms: 4 + -4 = 0 0 + r = 6.92820323 + -4 r = 6.92820323 + -4 Combine like terms: 6.92820323 + -4 = 2.92820323 r = 2.92820323 Simplifying r = 2.92820323Subproblem 2
r + 4 = -6.92820323 Simplifying r + 4 = -6.92820323 Reorder the terms: 4 + r = -6.92820323 Solving 4 + r = -6.92820323 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -6.92820323 + -4 Combine like terms: 4 + -4 = 0 0 + r = -6.92820323 + -4 r = -6.92820323 + -4 Combine like terms: -6.92820323 + -4 = -10.92820323 r = -10.92820323 Simplifying r = -10.92820323Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.92820323, -10.92820323}
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