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Simplifying (r + -4)(r + 18) = 4 Reorder the terms: (-4 + r)(r + 18) = 4 Reorder the terms: (-4 + r)(18 + r) = 4 Multiply (-4 + r) * (18 + r) (-4(18 + r) + r(18 + r)) = 4 ((18 * -4 + r * -4) + r(18 + r)) = 4 ((-72 + -4r) + r(18 + r)) = 4 (-72 + -4r + (18 * r + r * r)) = 4 (-72 + -4r + (18r + r2)) = 4 Combine like terms: -4r + 18r = 14r (-72 + 14r + r2) = 4 Solving -72 + 14r + r2 = 4 Solving for variable 'r'. Reorder the terms: -72 + -4 + 14r + r2 = 4 + -4 Combine like terms: -72 + -4 = -76 -76 + 14r + r2 = 4 + -4 Combine like terms: 4 + -4 = 0 -76 + 14r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 14r + 76 + r2 = 0 + 76 Reorder the terms: -76 + 76 + 14r + r2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 14r + r2 = 0 + 76 14r + r2 = 0 + 76 Combine like terms: 0 + 76 = 76 14r + r2 = 76 The r term is 14r. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14r + 49 + r2 = 76 + 49 Reorder the terms: 49 + 14r + r2 = 76 + 49 Combine like terms: 76 + 49 = 125 49 + 14r + r2 = 125 Factor a perfect square on the left side: (r + 7)(r + 7) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (r + 7) equal to 11.180339887 and -11.180339887.Subproblem 1
r + 7 = 11.180339887 Simplifying r + 7 = 11.180339887 Reorder the terms: 7 + r = 11.180339887 Solving 7 + r = 11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + r = 11.180339887 + -7 r = 11.180339887 + -7 Combine like terms: 11.180339887 + -7 = 4.180339887 r = 4.180339887 Simplifying r = 4.180339887Subproblem 2
r + 7 = -11.180339887 Simplifying r + 7 = -11.180339887 Reorder the terms: 7 + r = -11.180339887 Solving 7 + r = -11.180339887 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -11.180339887 + -7 Combine like terms: 7 + -7 = 0 0 + r = -11.180339887 + -7 r = -11.180339887 + -7 Combine like terms: -11.180339887 + -7 = -18.180339887 r = -18.180339887 Simplifying r = -18.180339887Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.180339887, -18.180339887}
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