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Simplifying r2 + 20r = 288 Reorder the terms: 20r + r2 = 288 Solving 20r + r2 = 288 Solving for variable 'r'. Reorder the terms: -288 + 20r + r2 = 288 + -288 Combine like terms: 288 + -288 = 0 -288 + 20r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + 20r + 288 + r2 = 0 + 288 Reorder the terms: -288 + 288 + 20r + r2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + 20r + r2 = 0 + 288 20r + r2 = 0 + 288 Combine like terms: 0 + 288 = 288 20r + r2 = 288 The r term is 20r. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20r + 100 + r2 = 288 + 100 Reorder the terms: 100 + 20r + r2 = 288 + 100 Combine like terms: 288 + 100 = 388 100 + 20r + r2 = 388 Factor a perfect square on the left side: (r + 10)(r + 10) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (r + 10) equal to 19.697715604 and -19.697715604.Subproblem 1
r + 10 = 19.697715604 Simplifying r + 10 = 19.697715604 Reorder the terms: 10 + r = 19.697715604 Solving 10 + r = 19.697715604 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + r = 19.697715604 + -10 Combine like terms: 10 + -10 = 0 0 + r = 19.697715604 + -10 r = 19.697715604 + -10 Combine like terms: 19.697715604 + -10 = 9.697715604 r = 9.697715604 Simplifying r = 9.697715604Subproblem 2
r + 10 = -19.697715604 Simplifying r + 10 = -19.697715604 Reorder the terms: 10 + r = -19.697715604 Solving 10 + r = -19.697715604 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + r = -19.697715604 + -10 Combine like terms: 10 + -10 = 0 0 + r = -19.697715604 + -10 r = -19.697715604 + -10 Combine like terms: -19.697715604 + -10 = -29.697715604 r = -29.697715604 Simplifying r = -29.697715604Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.697715604, -29.697715604}
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