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Simplifying 9r2 + -3r = 7r2 + 22 + 8r Reorder the terms: -3r + 9r2 = 7r2 + 22 + 8r Reorder the terms: -3r + 9r2 = 22 + 8r + 7r2 Solving -3r + 9r2 = 22 + 8r + 7r2 Solving for variable 'r'. Reorder the terms: -22 + -3r + -8r + 9r2 + -7r2 = 22 + 8r + 7r2 + -22 + -8r + -7r2 Combine like terms: -3r + -8r = -11r -22 + -11r + 9r2 + -7r2 = 22 + 8r + 7r2 + -22 + -8r + -7r2 Combine like terms: 9r2 + -7r2 = 2r2 -22 + -11r + 2r2 = 22 + 8r + 7r2 + -22 + -8r + -7r2 Reorder the terms: -22 + -11r + 2r2 = 22 + -22 + 8r + -8r + 7r2 + -7r2 Combine like terms: 22 + -22 = 0 -22 + -11r + 2r2 = 0 + 8r + -8r + 7r2 + -7r2 -22 + -11r + 2r2 = 8r + -8r + 7r2 + -7r2 Combine like terms: 8r + -8r = 0 -22 + -11r + 2r2 = 0 + 7r2 + -7r2 -22 + -11r + 2r2 = 7r2 + -7r2 Combine like terms: 7r2 + -7r2 = 0 -22 + -11r + 2r2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11 + -5.5r + r2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -5.5r + 11 + r2 = 0 + 11 Reorder the terms: -11 + 11 + -5.5r + r2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -5.5r + r2 = 0 + 11 -5.5r + r2 = 0 + 11 Combine like terms: 0 + 11 = 11 -5.5r + r2 = 11 The r term is -5.5r. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5r + 7.5625 + r2 = 11 + 7.5625 Reorder the terms: 7.5625 + -5.5r + r2 = 11 + 7.5625 Combine like terms: 11 + 7.5625 = 18.5625 7.5625 + -5.5r + r2 = 18.5625 Factor a perfect square on the left side: (r + -2.75)(r + -2.75) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (r + -2.75) equal to 4.308421985 and -4.308421985.Subproblem 1
r + -2.75 = 4.308421985 Simplifying r + -2.75 = 4.308421985 Reorder the terms: -2.75 + r = 4.308421985 Solving -2.75 + r = 4.308421985 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = 4.308421985 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = 4.308421985 + 2.75 r = 4.308421985 + 2.75 Combine like terms: 4.308421985 + 2.75 = 7.058421985 r = 7.058421985 Simplifying r = 7.058421985Subproblem 2
r + -2.75 = -4.308421985 Simplifying r + -2.75 = -4.308421985 Reorder the terms: -2.75 + r = -4.308421985 Solving -2.75 + r = -4.308421985 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + r = -4.308421985 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + r = -4.308421985 + 2.75 r = -4.308421985 + 2.75 Combine like terms: -4.308421985 + 2.75 = -1.558421985 r = -1.558421985 Simplifying r = -1.558421985Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.058421985, -1.558421985}
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