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Simplifying 0 = r2 + 10r + -301.6 Reorder the terms: 0 = -301.6 + 10r + r2 Solving 0 = -301.6 + 10r + r2 Solving for variable 'r'. Combine like terms: 0 + 301.6 = 301.6 301.6 + -10r + -1r2 = -301.6 + 10r + r2 + 301.6 + -10r + -1r2 Reorder the terms: 301.6 + -10r + -1r2 = -301.6 + 301.6 + 10r + -10r + r2 + -1r2 Combine like terms: -301.6 + 301.6 = 0.0 301.6 + -10r + -1r2 = 0.0 + 10r + -10r + r2 + -1r2 301.6 + -10r + -1r2 = 10r + -10r + r2 + -1r2 Combine like terms: 10r + -10r = 0 301.6 + -10r + -1r2 = 0 + r2 + -1r2 301.6 + -10r + -1r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 301.6 + -10r + -1r2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -301.6 + 10r + r2 = 0 Move the constant term to the right: Add '301.6' to each side of the equation. -301.6 + 10r + 301.6 + r2 = 0 + 301.6 Reorder the terms: -301.6 + 301.6 + 10r + r2 = 0 + 301.6 Combine like terms: -301.6 + 301.6 = 0.0 0.0 + 10r + r2 = 0 + 301.6 10r + r2 = 0 + 301.6 Combine like terms: 0 + 301.6 = 301.6 10r + r2 = 301.6 The r term is 10r. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10r + 25 + r2 = 301.6 + 25 Reorder the terms: 25 + 10r + r2 = 301.6 + 25 Combine like terms: 301.6 + 25 = 326.6 25 + 10r + r2 = 326.6 Factor a perfect square on the left side: (r + 5)(r + 5) = 326.6 Calculate the square root of the right side: 18.07207791 Break this problem into two subproblems by setting (r + 5) equal to 18.07207791 and -18.07207791.Subproblem 1
r + 5 = 18.07207791 Simplifying r + 5 = 18.07207791 Reorder the terms: 5 + r = 18.07207791 Solving 5 + r = 18.07207791 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 18.07207791 + -5 Combine like terms: 5 + -5 = 0 0 + r = 18.07207791 + -5 r = 18.07207791 + -5 Combine like terms: 18.07207791 + -5 = 13.07207791 r = 13.07207791 Simplifying r = 13.07207791Subproblem 2
r + 5 = -18.07207791 Simplifying r + 5 = -18.07207791 Reorder the terms: 5 + r = -18.07207791 Solving 5 + r = -18.07207791 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = -18.07207791 + -5 Combine like terms: 5 + -5 = 0 0 + r = -18.07207791 + -5 r = -18.07207791 + -5 Combine like terms: -18.07207791 + -5 = -23.07207791 r = -23.07207791 Simplifying r = -23.07207791Solution
The solution to the problem is based on the solutions from the subproblems. r = {13.07207791, -23.07207791}
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