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Simplifying r2 + 16r = -19 Reorder the terms: 16r + r2 = -19 Solving 16r + r2 = -19 Solving for variable 'r'. Reorder the terms: 19 + 16r + r2 = -19 + 19 Combine like terms: -19 + 19 = 0 19 + 16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 16r + -19 + r2 = 0 + -19 Reorder the terms: 19 + -19 + 16r + r2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 16r + r2 = 0 + -19 16r + r2 = 0 + -19 Combine like terms: 0 + -19 = -19 16r + r2 = -19 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 = -19 + 64 Reorder the terms: 64 + 16r + r2 = -19 + 64 Combine like terms: -19 + 64 = 45 64 + 16r + r2 = 45 Factor a perfect square on the left side: (r + 8)(r + 8) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (r + 8) equal to 6.708203933 and -6.708203933.Subproblem 1
r + 8 = 6.708203933 Simplifying r + 8 = 6.708203933 Reorder the terms: 8 + r = 6.708203933 Solving 8 + r = 6.708203933 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 = 6.708203933 + -8 Combine like terms: 8 + -8 = 0 0 + r = 6.708203933 + -8 r = 6.708203933 + -8 Combine like terms: 6.708203933 + -8 = -1.291796067 r = -1.291796067 Simplifying r = -1.291796067Subproblem 2
r + 8 = -6.708203933 Simplifying r + 8 = -6.708203933 Reorder the terms: 8 + r = -6.708203933 Solving 8 + r = -6.708203933 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 = -6.708203933 + -8 Combine like terms: 8 + -8 = 0 0 + r = -6.708203933 + -8 r = -6.708203933 + -8 Combine like terms: -6.708203933 + -8 = -14.708203933 r = -14.708203933 Simplifying r = -14.708203933Solution
The solution to the problem is based on the solutions from the subproblems. r = {-1.291796067, -14.708203933}
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