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Simplifying 9r2 + -340r + -655 = 0 Reorder the terms: -655 + -340r + 9r2 = 0 Solving -655 + -340r + 9r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -72.77777778 + -37.77777778r + r2 = 0 Move the constant term to the right: Add '72.77777778' to each side of the equation. -72.77777778 + -37.77777778r + 72.77777778 + r2 = 0 + 72.77777778 Reorder the terms: -72.77777778 + 72.77777778 + -37.77777778r + r2 = 0 + 72.77777778 Combine like terms: -72.77777778 + 72.77777778 = 0.00000000 0.00000000 + -37.77777778r + r2 = 0 + 72.77777778 -37.77777778r + r2 = 0 + 72.77777778 Combine like terms: 0 + 72.77777778 = 72.77777778 -37.77777778r + r2 = 72.77777778 The r term is -37.77777778r. Take half its coefficient (-18.88888889). Square it (356.7901235) and add it to both sides. Add '356.7901235' to each side of the equation. -37.77777778r + 356.7901235 + r2 = 72.77777778 + 356.7901235 Reorder the terms: 356.7901235 + -37.77777778r + r2 = 72.77777778 + 356.7901235 Combine like terms: 72.77777778 + 356.7901235 = 429.56790128 356.7901235 + -37.77777778r + r2 = 429.56790128 Factor a perfect square on the left side: (r + -18.88888889)(r + -18.88888889) = 429.56790128 Calculate the square root of the right side: 20.726019909 Break this problem into two subproblems by setting (r + -18.88888889) equal to 20.726019909 and -20.726019909.Subproblem 1
r + -18.88888889 = 20.726019909 Simplifying r + -18.88888889 = 20.726019909 Reorder the terms: -18.88888889 + r = 20.726019909 Solving -18.88888889 + r = 20.726019909 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '18.88888889' to each side of the equation. -18.88888889 + 18.88888889 + r = 20.726019909 + 18.88888889 Combine like terms: -18.88888889 + 18.88888889 = 0.00000000 0.00000000 + r = 20.726019909 + 18.88888889 r = 20.726019909 + 18.88888889 Combine like terms: 20.726019909 + 18.88888889 = 39.614908799 r = 39.614908799 Simplifying r = 39.614908799Subproblem 2
r + -18.88888889 = -20.726019909 Simplifying r + -18.88888889 = -20.726019909 Reorder the terms: -18.88888889 + r = -20.726019909 Solving -18.88888889 + r = -20.726019909 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '18.88888889' to each side of the equation. -18.88888889 + 18.88888889 + r = -20.726019909 + 18.88888889 Combine like terms: -18.88888889 + 18.88888889 = 0.00000000 0.00000000 + r = -20.726019909 + 18.88888889 r = -20.726019909 + 18.88888889 Combine like terms: -20.726019909 + 18.88888889 = -1.837131019 r = -1.837131019 Simplifying r = -1.837131019Solution
The solution to the problem is based on the solutions from the subproblems. r = {39.614908799, -1.837131019}
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