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Simplifying (r + -4)(r + 16) = -55 Reorder the terms: (-4 + r)(r + 16) = -55 Reorder the terms: (-4 + r)(16 + r) = -55 Multiply (-4 + r) * (16 + r) (-4(16 + r) + r(16 + r)) = -55 ((16 * -4 + r * -4) + r(16 + r)) = -55 ((-64 + -4r) + r(16 + r)) = -55 (-64 + -4r + (16 * r + r * r)) = -55 (-64 + -4r + (16r + r2)) = -55 Combine like terms: -4r + 16r = 12r (-64 + 12r + r2) = -55 Solving -64 + 12r + r2 = -55 Solving for variable 'r'. Reorder the terms: -64 + 55 + 12r + r2 = -55 + 55 Combine like terms: -64 + 55 = -9 -9 + 12r + r2 = -55 + 55 Combine like terms: -55 + 55 = 0 -9 + 12r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 12r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + 12r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 12r + r2 = 0 + 9 12r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 12r + r2 = 9 The r term is 12r. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12r + 36 + r2 = 9 + 36 Reorder the terms: 36 + 12r + r2 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + 12r + r2 = 45 Factor a perfect square on the left side: (r + 6)(r + 6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (r + 6) equal to 6.708203933 and -6.708203933.Subproblem 1
r + 6 = 6.708203933 Simplifying r + 6 = 6.708203933 Reorder the terms: 6 + r = 6.708203933 Solving 6 + r = 6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 6.708203933 + -6 Combine like terms: 6 + -6 = 0 0 + r = 6.708203933 + -6 r = 6.708203933 + -6 Combine like terms: 6.708203933 + -6 = 0.708203933 r = 0.708203933 Simplifying r = 0.708203933Subproblem 2
r + 6 = -6.708203933 Simplifying r + 6 = -6.708203933 Reorder the terms: 6 + r = -6.708203933 Solving 6 + r = -6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -6.708203933 + -6 Combine like terms: 6 + -6 = 0 0 + r = -6.708203933 + -6 r = -6.708203933 + -6 Combine like terms: -6.708203933 + -6 = -12.708203933 r = -12.708203933 Simplifying r = -12.708203933Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.708203933, -12.708203933}
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