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Simplifying r2 + 6r + -59 = 0 Reorder the terms: -59 + 6r + r2 = 0 Solving -59 + 6r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + 6r + 59 + r2 = 0 + 59 Reorder the terms: -59 + 59 + 6r + r2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 6r + r2 = 0 + 59 6r + r2 = 0 + 59 Combine like terms: 0 + 59 = 59 6r + r2 = 59 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 = 59 + 9 Reorder the terms: 9 + 6r + r2 = 59 + 9 Combine like terms: 59 + 9 = 68 9 + 6r + r2 = 68 Factor a perfect square on the left side: (r + 3)(r + 3) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (r + 3) equal to 8.246211251 and -8.246211251.Subproblem 1
r + 3 = 8.246211251 Simplifying r + 3 = 8.246211251 Reorder the terms: 3 + r = 8.246211251 Solving 3 + r = 8.246211251 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 = 8.246211251 + -3 Combine like terms: 3 + -3 = 0 0 + r = 8.246211251 + -3 r = 8.246211251 + -3 Combine like terms: 8.246211251 + -3 = 5.246211251 r = 5.246211251 Simplifying r = 5.246211251Subproblem 2
r + 3 = -8.246211251 Simplifying r + 3 = -8.246211251 Reorder the terms: 3 + r = -8.246211251 Solving 3 + r = -8.246211251 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 = -8.246211251 + -3 Combine like terms: 3 + -3 = 0 0 + r = -8.246211251 + -3 r = -8.246211251 + -3 Combine like terms: -8.246211251 + -3 = -11.246211251 r = -11.246211251 Simplifying r = -11.246211251Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.246211251, -11.246211251}
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