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Simplifying r2 + 10r + -900 = 0 Reorder the terms: -900 + 10r + r2 = 0 Solving -900 + 10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 10r + 900 + r2 = 0 + 900 Reorder the terms: -900 + 900 + 10r + r2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 10r + r2 = 0 + 900 10r + r2 = 0 + 900 Combine like terms: 0 + 900 = 900 10r + r2 = 900 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = 900 + 25 Reorder the terms: 25 + 10r + r2 = 900 + 25 Combine like terms: 900 + 25 = 925 25 + 10r + r2 = 925 Factor a perfect square on the left side: (r + 5)(r + 5) = 925 Calculate the square root of the right side: 30.413812651 Break this problem into two subproblems by setting (r + 5) equal to 30.413812651 and -30.413812651.Subproblem 1
r + 5 = 30.413812651 Simplifying r + 5 = 30.413812651 Reorder the terms: 5 + r = 30.413812651 Solving 5 + r = 30.413812651 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 30.413812651 + -5 Combine like terms: 5 + -5 = 0 0 + r = 30.413812651 + -5 r = 30.413812651 + -5 Combine like terms: 30.413812651 + -5 = 25.413812651 r = 25.413812651 Simplifying r = 25.413812651Subproblem 2
r + 5 = -30.413812651 Simplifying r + 5 = -30.413812651 Reorder the terms: 5 + r = -30.413812651 Solving 5 + r = -30.413812651 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -30.413812651 + -5 Combine like terms: 5 + -5 = 0 0 + r = -30.413812651 + -5 r = -30.413812651 + -5 Combine like terms: -30.413812651 + -5 = -35.413812651 r = -35.413812651 Simplifying r = -35.413812651Solution
The solution to the problem is based on the solutions from the subproblems. r = {25.413812651, -35.413812651}
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