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Simplifying r2 + -16r = 9 Reorder the terms: -16r + r2 = 9 Solving -16r + r2 = 9 Solving for variable 'r'. Reorder the terms: -9 + -16r + r2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -16r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -16r + 9 + r2 = 0 + 9 Reorder the terms: -9 + 9 + -16r + r2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -16r + r2 = 0 + 9 -16r + r2 = 0 + 9 Combine like terms: 0 + 9 = 9 -16r + r2 = 9 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 = 9 + 64 Reorder the terms: 64 + -16r + r2 = 9 + 64 Combine like terms: 9 + 64 = 73 64 + -16r + r2 = 73 Factor a perfect square on the left side: (r + -8)(r + -8) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (r + -8) equal to 8.544003745 and -8.544003745.Subproblem 1
r + -8 = 8.544003745 Simplifying r + -8 = 8.544003745 Reorder the terms: -8 + r = 8.544003745 Solving -8 + r = 8.544003745 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 = 8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + r = 8.544003745 + 8 r = 8.544003745 + 8 Combine like terms: 8.544003745 + 8 = 16.544003745 r = 16.544003745 Simplifying r = 16.544003745Subproblem 2
r + -8 = -8.544003745 Simplifying r + -8 = -8.544003745 Reorder the terms: -8 + r = -8.544003745 Solving -8 + r = -8.544003745 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 = -8.544003745 + 8 Combine like terms: -8 + 8 = 0 0 + r = -8.544003745 + 8 r = -8.544003745 + 8 Combine like terms: -8.544003745 + 8 = -0.544003745 r = -0.544003745 Simplifying r = -0.544003745Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.544003745, -0.544003745}
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