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Simplifying r2 + 40r + -2900 = 0 Reorder the terms: -2900 + 40r + r2 = 0 Solving -2900 + 40r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '2900' to each side of the equation. -2900 + 40r + 2900 + r2 = 0 + 2900 Reorder the terms: -2900 + 2900 + 40r + r2 = 0 + 2900 Combine like terms: -2900 + 2900 = 0 0 + 40r + r2 = 0 + 2900 40r + r2 = 0 + 2900 Combine like terms: 0 + 2900 = 2900 40r + r2 = 2900 The r term is 40r. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40r + 400 + r2 = 2900 + 400 Reorder the terms: 400 + 40r + r2 = 2900 + 400 Combine like terms: 2900 + 400 = 3300 400 + 40r + r2 = 3300 Factor a perfect square on the left side: (r + 20)(r + 20) = 3300 Calculate the square root of the right side: 57.445626465 Break this problem into two subproblems by setting (r + 20) equal to 57.445626465 and -57.445626465.Subproblem 1
r + 20 = 57.445626465 Simplifying r + 20 = 57.445626465 Reorder the terms: 20 + r = 57.445626465 Solving 20 + r = 57.445626465 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = 57.445626465 + -20 Combine like terms: 20 + -20 = 0 0 + r = 57.445626465 + -20 r = 57.445626465 + -20 Combine like terms: 57.445626465 + -20 = 37.445626465 r = 37.445626465 Simplifying r = 37.445626465Subproblem 2
r + 20 = -57.445626465 Simplifying r + 20 = -57.445626465 Reorder the terms: 20 + r = -57.445626465 Solving 20 + r = -57.445626465 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + r = -57.445626465 + -20 Combine like terms: 20 + -20 = 0 0 + r = -57.445626465 + -20 r = -57.445626465 + -20 Combine like terms: -57.445626465 + -20 = -77.445626465 r = -77.445626465 Simplifying r = -77.445626465Solution
The solution to the problem is based on the solutions from the subproblems. r = {37.445626465, -77.445626465}
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