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Simplifying r2 + -8r = -8 Reorder the terms: -8r + r2 = -8 Solving -8r + r2 = -8 Solving for variable 'r'. Reorder the terms: 8 + -8r + r2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + -8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8r + -8 + r2 = 0 + -8 Reorder the terms: 8 + -8 + -8r + r2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8r + r2 = 0 + -8 -8r + r2 = 0 + -8 Combine like terms: 0 + -8 = -8 -8r + r2 = -8 The r term is -8r. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8r + 16 + r2 = -8 + 16 Reorder the terms: 16 + -8r + r2 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + -8r + r2 = 8 Factor a perfect square on the left side: (r + -4)(r + -4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (r + -4) equal to 2.828427125 and -2.828427125.Subproblem 1
r + -4 = 2.828427125 Simplifying r + -4 = 2.828427125 Reorder the terms: -4 + r = 2.828427125 Solving -4 + r = 2.828427125 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = 2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + r = 2.828427125 + 4 r = 2.828427125 + 4 Combine like terms: 2.828427125 + 4 = 6.828427125 r = 6.828427125 Simplifying r = 6.828427125Subproblem 2
r + -4 = -2.828427125 Simplifying r + -4 = -2.828427125 Reorder the terms: -4 + r = -2.828427125 Solving -4 + r = -2.828427125 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + r = -2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + r = -2.828427125 + 4 r = -2.828427125 + 4 Combine like terms: -2.828427125 + 4 = 1.171572875 r = 1.171572875 Simplifying r = 1.171572875Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.828427125, 1.171572875}
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