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Simplifying 0 = r2 + 14r + -219.8 Reorder the terms: 0 = -219.8 + 14r + r2 Solving 0 = -219.8 + 14r + r2 Solving for variable 'r'. Combine like terms: 0 + 219.8 = 219.8 219.8 + -14r + -1r2 = -219.8 + 14r + r2 + 219.8 + -14r + -1r2 Reorder the terms: 219.8 + -14r + -1r2 = -219.8 + 219.8 + 14r + -14r + r2 + -1r2 Combine like terms: -219.8 + 219.8 = 0.0 219.8 + -14r + -1r2 = 0.0 + 14r + -14r + r2 + -1r2 219.8 + -14r + -1r2 = 14r + -14r + r2 + -1r2 Combine like terms: 14r + -14r = 0 219.8 + -14r + -1r2 = 0 + r2 + -1r2 219.8 + -14r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 219.8 + -14r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -219.8 + 14r + r2 = 0 Move the constant term to the right: Add '219.8' to each side of the equation. -219.8 + 14r + 219.8 + r2 = 0 + 219.8 Reorder the terms: -219.8 + 219.8 + 14r + r2 = 0 + 219.8 Combine like terms: -219.8 + 219.8 = 0.0 0.0 + 14r + r2 = 0 + 219.8 14r + r2 = 0 + 219.8 Combine like terms: 0 + 219.8 = 219.8 14r + r2 = 219.8 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 = 219.8 + 49 Reorder the terms: 49 + 14r + r2 = 219.8 + 49 Combine like terms: 219.8 + 49 = 268.8 49 + 14r + r2 = 268.8 Factor a perfect square on the left side: (r + 7)(r + 7) = 268.8 Calculate the square root of the right side: 16.395121226 Break this problem into two subproblems by setting (r + 7) equal to 16.395121226 and -16.395121226.Subproblem 1
r + 7 = 16.395121226 Simplifying r + 7 = 16.395121226 Reorder the terms: 7 + r = 16.395121226 Solving 7 + r = 16.395121226 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 = 16.395121226 + -7 Combine like terms: 7 + -7 = 0 0 + r = 16.395121226 + -7 r = 16.395121226 + -7 Combine like terms: 16.395121226 + -7 = 9.395121226 r = 9.395121226 Simplifying r = 9.395121226Subproblem 2
r + 7 = -16.395121226 Simplifying r + 7 = -16.395121226 Reorder the terms: 7 + r = -16.395121226 Solving 7 + r = -16.395121226 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 = -16.395121226 + -7 Combine like terms: 7 + -7 = 0 0 + r = -16.395121226 + -7 r = -16.395121226 + -7 Combine like terms: -16.395121226 + -7 = -23.395121226 r = -23.395121226 Simplifying r = -23.395121226Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.395121226, -23.395121226}
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