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Simplifying r2 + 8r = 21 Reorder the terms: 8r + r2 = 21 Solving 8r + r2 = 21 Solving for variable 'r'. Reorder the terms: -21 + 8r + r2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + 8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 8r + 21 + r2 = 0 + 21 Reorder the terms: -21 + 21 + 8r + r2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 8r + r2 = 0 + 21 8r + r2 = 0 + 21 Combine like terms: 0 + 21 = 21 8r + r2 = 21 The r term is 8r. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8r + 16 + r2 = 21 + 16 Reorder the terms: 16 + 8r + r2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + 8r + r2 = 37 Factor a perfect square on the left side: (r + 4)(r + 4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (r + 4) equal to 6.08276253 and -6.08276253.Subproblem 1
r + 4 = 6.08276253 Simplifying r + 4 = 6.08276253 Reorder the terms: 4 + r = 6.08276253 Solving 4 + r = 6.08276253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + r = 6.08276253 + -4 r = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 r = 2.08276253 Simplifying r = 2.08276253Subproblem 2
r + 4 = -6.08276253 Simplifying r + 4 = -6.08276253 Reorder the terms: 4 + r = -6.08276253 Solving 4 + r = -6.08276253 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + r = -6.08276253 + -4 r = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 r = -10.08276253 Simplifying r = -10.08276253Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.08276253, -10.08276253}
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