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Simplifying r2 + 16r + 10 = 0 Reorder the terms: 10 + 16r + r2 = 0 Solving 10 + 16r + 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 + 16r + -10 + r2 = 0 + -10 Reorder the terms: 10 + -10 + 16r + r2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 16r + r2 = 0 + -10 16r + r2 = 0 + -10 Combine like terms: 0 + -10 = -10 16r + r2 = -10 The r term is 16r. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16r + 64 + r2 = -10 + 64 Reorder the terms: 64 + 16r + r2 = -10 + 64 Combine like terms: -10 + 64 = 54 64 + 16r + r2 = 54 Factor a perfect square on the left side: (r + 8)(r + 8) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (r + 8) equal to 7.348469228 and -7.348469228.Subproblem 1
r + 8 = 7.348469228 Simplifying r + 8 = 7.348469228 Reorder the terms: 8 + r = 7.348469228 Solving 8 + r = 7.348469228 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 7.348469228 + -8 Combine like terms: 8 + -8 = 0 0 + r = 7.348469228 + -8 r = 7.348469228 + -8 Combine like terms: 7.348469228 + -8 = -0.651530772 r = -0.651530772 Simplifying r = -0.651530772Subproblem 2
r + 8 = -7.348469228 Simplifying r + 8 = -7.348469228 Reorder the terms: 8 + r = -7.348469228 Solving 8 + r = -7.348469228 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -7.348469228 + -8 Combine like terms: 8 + -8 = 0 0 + r = -7.348469228 + -8 r = -7.348469228 + -8 Combine like terms: -7.348469228 + -8 = -15.348469228 r = -15.348469228 Simplifying r = -15.348469228Solution
The solution to the problem is based on the solutions from the subproblems. r = {-0.651530772, -15.348469228}
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