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Simplifying r2 + 21r + 10 = 0 Reorder the terms: 10 + 21r + r2 = 0 Solving 10 + 21r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 21r + -10 + r2 = 0 + -10 Reorder the terms: 10 + -10 + 21r + r2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 21r + r2 = 0 + -10 21r + r2 = 0 + -10 Combine like terms: 0 + -10 = -10 21r + r2 = -10 The r term is 21r. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21r + 110.25 + r2 = -10 + 110.25 Reorder the terms: 110.25 + 21r + r2 = -10 + 110.25 Combine like terms: -10 + 110.25 = 100.25 110.25 + 21r + r2 = 100.25 Factor a perfect square on the left side: (r + 10.5)(r + 10.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (r + 10.5) equal to 10.012492197 and -10.012492197.Subproblem 1
r + 10.5 = 10.012492197 Simplifying r + 10.5 = 10.012492197 Reorder the terms: 10.5 + r = 10.012492197 Solving 10.5 + r = 10.012492197 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + r = 10.012492197 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + r = 10.012492197 + -10.5 r = 10.012492197 + -10.5 Combine like terms: 10.012492197 + -10.5 = -0.487507803 r = -0.487507803 Simplifying r = -0.487507803Subproblem 2
r + 10.5 = -10.012492197 Simplifying r + 10.5 = -10.012492197 Reorder the terms: 10.5 + r = -10.012492197 Solving 10.5 + r = -10.012492197 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + r = -10.012492197 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + r = -10.012492197 + -10.5 r = -10.012492197 + -10.5 Combine like terms: -10.012492197 + -10.5 = -20.512492197 r = -20.512492197 Simplifying r = -20.512492197Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.487507803, -20.512492197}
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