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Simplifying r2 + -16r + 64 = 54 Reorder the terms: 64 + -16r + r2 = 54 Solving 64 + -16r + r2 = 54 Solving for variable 'r'. Reorder the terms: 64 + -54 + -16r + r2 = 54 + -54 Combine like terms: 64 + -54 = 10 10 + -16r + r2 = 54 + -54 Combine like terms: 54 + -54 = 0 10 + -16r + r2 = 0 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 = 15.348469228 r = 15.348469228 Simplifying r = 15.348469228Subproblem 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 = 0.651530772 r = 0.651530772 Simplifying r = 0.651530772Solution
The solution to the problem is based on the solutions from the subproblems. r = {15.348469228, 0.651530772}
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