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Simplifying r2 + 12r + 26 = 0 Reorder the terms: 26 + 12r + r2 = 0 Solving 26 + 12r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 12r + -26 + r2 = 0 + -26 Reorder the terms: 26 + -26 + 12r + r2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 12r + r2 = 0 + -26 12r + r2 = 0 + -26 Combine like terms: 0 + -26 = -26 12r + r2 = -26 The r term is 12r. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12r + 36 + r2 = -26 + 36 Reorder the terms: 36 + 12r + r2 = -26 + 36 Combine like terms: -26 + 36 = 10 36 + 12r + r2 = 10 Factor a perfect square on the left side: (r + 6)(r + 6) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (r + 6) equal to 3.16227766 and -3.16227766.Subproblem 1
r + 6 = 3.16227766 Simplifying r + 6 = 3.16227766 Reorder the terms: 6 + r = 3.16227766 Solving 6 + r = 3.16227766 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = 3.16227766 + -6 Combine like terms: 6 + -6 = 0 0 + r = 3.16227766 + -6 r = 3.16227766 + -6 Combine like terms: 3.16227766 + -6 = -2.83772234 r = -2.83772234 Simplifying r = -2.83772234Subproblem 2
r + 6 = -3.16227766 Simplifying r + 6 = -3.16227766 Reorder the terms: 6 + r = -3.16227766 Solving 6 + r = -3.16227766 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + r = -3.16227766 + -6 Combine like terms: 6 + -6 = 0 0 + r = -3.16227766 + -6 r = -3.16227766 + -6 Combine like terms: -3.16227766 + -6 = -9.16227766 r = -9.16227766 Simplifying r = -9.16227766Solution
The solution to the problem is based on the solutions from the subproblems. r = {-2.83772234, -9.16227766}
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