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Simplifying 188.4 = 3.14r * 10 + 3.14r2 Reorder the terms for easier multiplication: 188.4 = 3.14 * 10r + 3.14r2 Multiply 3.14 * 10 188.4 = 31.4r + 3.14r2 Solving 188.4 = 31.4r + 3.14r2 Solving for variable 'r'. Reorder the terms: 188.4 + -31.4r + -3.14r2 = 31.4r + -31.4r + 3.14r2 + -3.14r2 Combine like terms: 31.4r + -31.4r = 0.0 188.4 + -31.4r + -3.14r2 = 0.0 + 3.14r2 + -3.14r2 188.4 + -31.4r + -3.14r2 = 3.14r2 + -3.14r2 Combine like terms: 3.14r2 + -3.14r2 = 0.00 188.4 + -31.4r + -3.14r2 = 0.00 Begin completing the square. Divide all terms by -3.14 the coefficient of the squared term: Divide each side by '-3.14'. -60 + 10r + r2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 10r + 60 + r2 = 0 + 60 Reorder the terms: -60 + 60 + 10r + r2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 10r + r2 = 0 + 60 10r + r2 = 0 + 60 Combine like terms: 0 + 60 = 60 10r + r2 = 60 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 = 60 + 25 Reorder the terms: 25 + 10r + r2 = 60 + 25 Combine like terms: 60 + 25 = 85 25 + 10r + r2 = 85 Factor a perfect square on the left side: (r + 5)(r + 5) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (r + 5) equal to 9.219544457 and -9.219544457.Subproblem 1
r + 5 = 9.219544457 Simplifying r + 5 = 9.219544457 Reorder the terms: 5 + r = 9.219544457 Solving 5 + r = 9.219544457 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 = 9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + r = 9.219544457 + -5 r = 9.219544457 + -5 Combine like terms: 9.219544457 + -5 = 4.219544457 r = 4.219544457 Simplifying r = 4.219544457Subproblem 2
r + 5 = -9.219544457 Simplifying r + 5 = -9.219544457 Reorder the terms: 5 + r = -9.219544457 Solving 5 + r = -9.219544457 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 = -9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + r = -9.219544457 + -5 r = -9.219544457 + -5 Combine like terms: -9.219544457 + -5 = -14.219544457 r = -14.219544457 Simplifying r = -14.219544457Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.219544457, -14.219544457}
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