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Simplifying r2 = 16r + 5 Reorder the terms: r2 = 5 + 16r Solving r2 = 5 + 16r Solving for variable 'r'. Reorder the terms: -5 + -16r + r2 = 5 + 16r + -5 + -16r Reorder the terms: -5 + -16r + r2 = 5 + -5 + 16r + -16r Combine like terms: 5 + -5 = 0 -5 + -16r + r2 = 0 + 16r + -16r -5 + -16r + r2 = 16r + -16r Combine like terms: 16r + -16r = 0 -5 + -16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -16r + 5 + r2 = 0 + 5 Reorder the terms: -5 + 5 + -16r + r2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -16r + r2 = 0 + 5 -16r + r2 = 0 + 5 Combine like terms: 0 + 5 = 5 -16r + r2 = 5 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 = 5 + 64 Reorder the terms: 64 + -16r + r2 = 5 + 64 Combine like terms: 5 + 64 = 69 64 + -16r + r2 = 69 Factor a perfect square on the left side: (r + -8)(r + -8) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (r + -8) equal to 8.306623863 and -8.306623863.Subproblem 1
r + -8 = 8.306623863 Simplifying r + -8 = 8.306623863 Reorder the terms: -8 + r = 8.306623863 Solving -8 + r = 8.306623863 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 = 8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + r = 8.306623863 + 8 r = 8.306623863 + 8 Combine like terms: 8.306623863 + 8 = 16.306623863 r = 16.306623863 Simplifying r = 16.306623863Subproblem 2
r + -8 = -8.306623863 Simplifying r + -8 = -8.306623863 Reorder the terms: -8 + r = -8.306623863 Solving -8 + r = -8.306623863 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 = -8.306623863 + 8 Combine like terms: -8 + 8 = 0 0 + r = -8.306623863 + 8 r = -8.306623863 + 8 Combine like terms: -8.306623863 + 8 = -0.306623863 r = -0.306623863 Simplifying r = -0.306623863Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.306623863, -0.306623863}
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