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Simplifying r2 + 6r + 8 = 10 Reorder the terms: 8 + 6r + r2 = 10 Solving 8 + 6r + r2 = 10 Solving for variable 'r'. Reorder the terms: 8 + -10 + 6r + r2 = 10 + -10 Combine like terms: 8 + -10 = -2 -2 + 6r + r2 = 10 + -10 Combine like terms: 10 + -10 = 0 -2 + 6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 6r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + 6r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6r + r2 = 0 + 2 6r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 6r + r2 = 2 The r term is 6r. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6r + 9 + r2 = 2 + 9 Reorder the terms: 9 + 6r + r2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6r + r2 = 11 Factor a perfect square on the left side: (r + 3)(r + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (r + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
r + 3 = 3.31662479 Simplifying r + 3 = 3.31662479 Reorder the terms: 3 + r = 3.31662479 Solving 3 + r = 3.31662479 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + r = 3.31662479 + -3 r = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 r = 0.31662479 Simplifying r = 0.31662479Subproblem 2
r + 3 = -3.31662479 Simplifying r + 3 = -3.31662479 Reorder the terms: 3 + r = -3.31662479 Solving 3 + r = -3.31662479 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + r = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + r = -3.31662479 + -3 r = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 r = -6.31662479 Simplifying r = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.31662479, -6.31662479}
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