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Simplifying r2 + -8r + -79 = 6 Reorder the terms: -79 + -8r + r2 = 6 Solving -79 + -8r + r2 = 6 Solving for variable 'r'. Reorder the terms: -79 + -6 + -8r + r2 = 6 + -6 Combine like terms: -79 + -6 = -85 -85 + -8r + r2 = 6 + -6 Combine like terms: 6 + -6 = 0 -85 + -8r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + -8r + 85 + r2 = 0 + 85 Reorder the terms: -85 + 85 + -8r + r2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + -8r + r2 = 0 + 85 -8r + r2 = 0 + 85 Combine like terms: 0 + 85 = 85 -8r + r2 = 85 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 = 85 + 16 Reorder the terms: 16 + -8r + r2 = 85 + 16 Combine like terms: 85 + 16 = 101 16 + -8r + r2 = 101 Factor a perfect square on the left side: (r + -4)(r + -4) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (r + -4) equal to 10.049875621 and -10.049875621.Subproblem 1
r + -4 = 10.049875621 Simplifying r + -4 = 10.049875621 Reorder the terms: -4 + r = 10.049875621 Solving -4 + r = 10.049875621 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 = 10.049875621 + 4 Combine like terms: -4 + 4 = 0 0 + r = 10.049875621 + 4 r = 10.049875621 + 4 Combine like terms: 10.049875621 + 4 = 14.049875621 r = 14.049875621 Simplifying r = 14.049875621Subproblem 2
r + -4 = -10.049875621 Simplifying r + -4 = -10.049875621 Reorder the terms: -4 + r = -10.049875621 Solving -4 + r = -10.049875621 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 = -10.049875621 + 4 Combine like terms: -4 + 4 = 0 0 + r = -10.049875621 + 4 r = -10.049875621 + 4 Combine like terms: -10.049875621 + 4 = -6.049875621 r = -6.049875621 Simplifying r = -6.049875621Solution
The solution to the problem is based on the solutions from the subproblems. r = {14.049875621, -6.049875621}
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