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Simplifying r2 + 19r + -18 = 0 Reorder the terms: -18 + 19r + r2 = 0 Solving -18 + 19r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 19r + 18 + r2 = 0 + 18 Reorder the terms: -18 + 18 + 19r + r2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 19r + r2 = 0 + 18 19r + r2 = 0 + 18 Combine like terms: 0 + 18 = 18 19r + r2 = 18 The r term is 19r. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19r + 90.25 + r2 = 18 + 90.25 Reorder the terms: 90.25 + 19r + r2 = 18 + 90.25 Combine like terms: 18 + 90.25 = 108.25 90.25 + 19r + r2 = 108.25 Factor a perfect square on the left side: (r + 9.5)(r + 9.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (r + 9.5) equal to 10.404326023 and -10.404326023.Subproblem 1
r + 9.5 = 10.404326023 Simplifying r + 9.5 = 10.404326023 Reorder the terms: 9.5 + r = 10.404326023 Solving 9.5 + r = 10.404326023 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + r = 10.404326023 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + r = 10.404326023 + -9.5 r = 10.404326023 + -9.5 Combine like terms: 10.404326023 + -9.5 = 0.904326023 r = 0.904326023 Simplifying r = 0.904326023Subproblem 2
r + 9.5 = -10.404326023 Simplifying r + 9.5 = -10.404326023 Reorder the terms: 9.5 + r = -10.404326023 Solving 9.5 + r = -10.404326023 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + r = -10.404326023 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + r = -10.404326023 + -9.5 r = -10.404326023 + -9.5 Combine like terms: -10.404326023 + -9.5 = -19.904326023 r = -19.904326023 Simplifying r = -19.904326023Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.904326023, -19.904326023}
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