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Simplifying r2 + 64 = r + 144 Reorder the terms: 64 + r2 = r + 144 Reorder the terms: 64 + r2 = 144 + r Solving 64 + r2 = 144 + r Solving for variable 'r'. Reorder the terms: 64 + -144 + -1r + r2 = 144 + r + -144 + -1r Combine like terms: 64 + -144 = -80 -80 + -1r + r2 = 144 + r + -144 + -1r Reorder the terms: -80 + -1r + r2 = 144 + -144 + r + -1r Combine like terms: 144 + -144 = 0 -80 + -1r + r2 = 0 + r + -1r -80 + -1r + r2 = r + -1r Combine like terms: r + -1r = 0 -80 + -1r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -1r + 80 + r2 = 0 + 80 Reorder the terms: -80 + 80 + -1r + r2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -1r + r2 = 0 + 80 -1r + r2 = 0 + 80 Combine like terms: 0 + 80 = 80 -1r + r2 = 80 The r term is -1r. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1r + 0.25 + r2 = 80 + 0.25 Reorder the terms: 0.25 + -1r + r2 = 80 + 0.25 Combine like terms: 80 + 0.25 = 80.25 0.25 + -1r + r2 = 80.25 Factor a perfect square on the left side: (r + -0.5)(r + -0.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (r + -0.5) equal to 8.958236434 and -8.958236434.Subproblem 1
r + -0.5 = 8.958236434 Simplifying r + -0.5 = 8.958236434 Reorder the terms: -0.5 + r = 8.958236434 Solving -0.5 + r = 8.958236434 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 8.958236434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 8.958236434 + 0.5 r = 8.958236434 + 0.5 Combine like terms: 8.958236434 + 0.5 = 9.458236434 r = 9.458236434 Simplifying r = 9.458236434Subproblem 2
r + -0.5 = -8.958236434 Simplifying r + -0.5 = -8.958236434 Reorder the terms: -0.5 + r = -8.958236434 Solving -0.5 + r = -8.958236434 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -8.958236434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -8.958236434 + 0.5 r = -8.958236434 + 0.5 Combine like terms: -8.958236434 + 0.5 = -8.458236434 r = -8.458236434 Simplifying r = -8.458236434Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.458236434, -8.458236434}
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