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Simplifying (r + -3)(r + 15) = 4 Reorder the terms: (-3 + r)(r + 15) = 4 Reorder the terms: (-3 + r)(15 + r) = 4 Multiply (-3 + r) * (15 + r) (-3(15 + r) + r(15 + r)) = 4 ((15 * -3 + r * -3) + r(15 + r)) = 4 ((-45 + -3r) + r(15 + r)) = 4 (-45 + -3r + (15 * r + r * r)) = 4 (-45 + -3r + (15r + r2)) = 4 Combine like terms: -3r + 15r = 12r (-45 + 12r + r2) = 4 Solving -45 + 12r + r2 = 4 Solving for variable 'r'. Reorder the terms: -45 + -4 + 12r + r2 = 4 + -4 Combine like terms: -45 + -4 = -49 -49 + 12r + r2 = 4 + -4 Combine like terms: 4 + -4 = 0 -49 + 12r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 12r + 49 + r2 = 0 + 49 Reorder the terms: -49 + 49 + 12r + r2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 12r + r2 = 0 + 49 12r + r2 = 0 + 49 Combine like terms: 0 + 49 = 49 12r + r2 = 49 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 = 49 + 36 Reorder the terms: 36 + 12r + r2 = 49 + 36 Combine like terms: 49 + 36 = 85 36 + 12r + r2 = 85 Factor a perfect square on the left side: (r + 6)(r + 6) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (r + 6) equal to 9.219544457 and -9.219544457.Subproblem 1
r + 6 = 9.219544457 Simplifying r + 6 = 9.219544457 Reorder the terms: 6 + r = 9.219544457 Solving 6 + r = 9.219544457 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 = 9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + r = 9.219544457 + -6 r = 9.219544457 + -6 Combine like terms: 9.219544457 + -6 = 3.219544457 r = 3.219544457 Simplifying r = 3.219544457Subproblem 2
r + 6 = -9.219544457 Simplifying r + 6 = -9.219544457 Reorder the terms: 6 + r = -9.219544457 Solving 6 + r = -9.219544457 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 = -9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + r = -9.219544457 + -6 r = -9.219544457 + -6 Combine like terms: -9.219544457 + -6 = -15.219544457 r = -15.219544457 Simplifying r = -15.219544457Solution
The solution to the problem is based on the solutions from the subproblems. r = {3.219544457, -15.219544457}
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