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Simplifying r2 + 36r + -512 = 0 Reorder the terms: -512 + 36r + r2 = 0 Solving -512 + 36r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '512' to each side of the equation. -512 + 36r + 512 + r2 = 0 + 512 Reorder the terms: -512 + 512 + 36r + r2 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + 36r + r2 = 0 + 512 36r + r2 = 0 + 512 Combine like terms: 0 + 512 = 512 36r + r2 = 512 The r term is 36r. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36r + 324 + r2 = 512 + 324 Reorder the terms: 324 + 36r + r2 = 512 + 324 Combine like terms: 512 + 324 = 836 324 + 36r + r2 = 836 Factor a perfect square on the left side: (r + 18)(r + 18) = 836 Calculate the square root of the right side: 28.91366459 Break this problem into two subproblems by setting (r + 18) equal to 28.91366459 and -28.91366459.Subproblem 1
r + 18 = 28.91366459 Simplifying r + 18 = 28.91366459 Reorder the terms: 18 + r = 28.91366459 Solving 18 + r = 28.91366459 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + r = 28.91366459 + -18 Combine like terms: 18 + -18 = 0 0 + r = 28.91366459 + -18 r = 28.91366459 + -18 Combine like terms: 28.91366459 + -18 = 10.91366459 r = 10.91366459 Simplifying r = 10.91366459Subproblem 2
r + 18 = -28.91366459 Simplifying r + 18 = -28.91366459 Reorder the terms: 18 + r = -28.91366459 Solving 18 + r = -28.91366459 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + r = -28.91366459 + -18 Combine like terms: 18 + -18 = 0 0 + r = -28.91366459 + -18 r = -28.91366459 + -18 Combine like terms: -28.91366459 + -18 = -46.91366459 r = -46.91366459 Simplifying r = -46.91366459Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.91366459, -46.91366459}
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