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Simplifying r2 + 14r + 21 = 0 Reorder the terms: 21 + 14r + r2 = 0 Solving 21 + 14r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 14r + -21 + r2 = 0 + -21 Reorder the terms: 21 + -21 + 14r + r2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 14r + r2 = 0 + -21 14r + r2 = 0 + -21 Combine like terms: 0 + -21 = -21 14r + r2 = -21 The r term is 14r. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14r + 49 + r2 = -21 + 49 Reorder the terms: 49 + 14r + r2 = -21 + 49 Combine like terms: -21 + 49 = 28 49 + 14r + r2 = 28 Factor a perfect square on the left side: (r + 7)(r + 7) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (r + 7) equal to 5.291502622 and -5.291502622.Subproblem 1
r + 7 = 5.291502622 Simplifying r + 7 = 5.291502622 Reorder the terms: 7 + r = 5.291502622 Solving 7 + r = 5.291502622 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = 5.291502622 + -7 Combine like terms: 7 + -7 = 0 0 + r = 5.291502622 + -7 r = 5.291502622 + -7 Combine like terms: 5.291502622 + -7 = -1.708497378 r = -1.708497378 Simplifying r = -1.708497378Subproblem 2
r + 7 = -5.291502622 Simplifying r + 7 = -5.291502622 Reorder the terms: 7 + r = -5.291502622 Solving 7 + r = -5.291502622 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + r = -5.291502622 + -7 Combine like terms: 7 + -7 = 0 0 + r = -5.291502622 + -7 r = -5.291502622 + -7 Combine like terms: -5.291502622 + -7 = -12.291502622 r = -12.291502622 Simplifying r = -12.291502622Solution
The solution to the problem is based on the solutions from the subproblems. r = {-1.708497378, -12.291502622}
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