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Simplifying (r + -3)(r + 11) = -4 Reorder the terms: (-3 + r)(r + 11) = -4 Reorder the terms: (-3 + r)(11 + r) = -4 Multiply (-3 + r) * (11 + r) (-3(11 + r) + r(11 + r)) = -4 ((11 * -3 + r * -3) + r(11 + r)) = -4 ((-33 + -3r) + r(11 + r)) = -4 (-33 + -3r + (11 * r + r * r)) = -4 (-33 + -3r + (11r + r2)) = -4 Combine like terms: -3r + 11r = 8r (-33 + 8r + r2) = -4 Solving -33 + 8r + r2 = -4 Solving for variable 'r'. Reorder the terms: -33 + 4 + 8r + r2 = -4 + 4 Combine like terms: -33 + 4 = -29 -29 + 8r + r2 = -4 + 4 Combine like terms: -4 + 4 = 0 -29 + 8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 8r + 29 + r2 = 0 + 29 Reorder the terms: -29 + 29 + 8r + r2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 8r + r2 = 0 + 29 8r + r2 = 0 + 29 Combine like terms: 0 + 29 = 29 8r + r2 = 29 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 = 29 + 16 Reorder the terms: 16 + 8r + r2 = 29 + 16 Combine like terms: 29 + 16 = 45 16 + 8r + r2 = 45 Factor a perfect square on the left side: (r + 4)(r + 4) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (r + 4) equal to 6.708203933 and -6.708203933.Subproblem 1
r + 4 = 6.708203933 Simplifying r + 4 = 6.708203933 Reorder the terms: 4 + r = 6.708203933 Solving 4 + r = 6.708203933 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 = 6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + r = 6.708203933 + -4 r = 6.708203933 + -4 Combine like terms: 6.708203933 + -4 = 2.708203933 r = 2.708203933 Simplifying r = 2.708203933Subproblem 2
r + 4 = -6.708203933 Simplifying r + 4 = -6.708203933 Reorder the terms: 4 + r = -6.708203933 Solving 4 + r = -6.708203933 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 = -6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + r = -6.708203933 + -4 r = -6.708203933 + -4 Combine like terms: -6.708203933 + -4 = -10.708203933 r = -10.708203933 Simplifying r = -10.708203933Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.708203933, -10.708203933}
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