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Simplifying r2 + -39 = 16r Reorder the terms: -39 + r2 = 16r Solving -39 + r2 = 16r Solving for variable 'r'. Reorder the terms: -39 + -16r + r2 = 16r + -16r Combine like terms: 16r + -16r = 0 -39 + -16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -16r + 39 + r2 = 0 + 39 Reorder the terms: -39 + 39 + -16r + r2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -16r + r2 = 0 + 39 -16r + r2 = 0 + 39 Combine like terms: 0 + 39 = 39 -16r + r2 = 39 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 = 39 + 64 Reorder the terms: 64 + -16r + r2 = 39 + 64 Combine like terms: 39 + 64 = 103 64 + -16r + r2 = 103 Factor a perfect square on the left side: (r + -8)(r + -8) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (r + -8) equal to 10.148891565 and -10.148891565.Subproblem 1
r + -8 = 10.148891565 Simplifying r + -8 = 10.148891565 Reorder the terms: -8 + r = 10.148891565 Solving -8 + r = 10.148891565 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 = 10.148891565 + 8 Combine like terms: -8 + 8 = 0 0 + r = 10.148891565 + 8 r = 10.148891565 + 8 Combine like terms: 10.148891565 + 8 = 18.148891565 r = 18.148891565 Simplifying r = 18.148891565Subproblem 2
r + -8 = -10.148891565 Simplifying r + -8 = -10.148891565 Reorder the terms: -8 + r = -10.148891565 Solving -8 + r = -10.148891565 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 = -10.148891565 + 8 Combine like terms: -8 + 8 = 0 0 + r = -10.148891565 + 8 r = -10.148891565 + 8 Combine like terms: -10.148891565 + 8 = -2.148891565 r = -2.148891565 Simplifying r = -2.148891565Solution
The solution to the problem is based on the solutions from the subproblems. r = {18.148891565, -2.148891565}
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