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Simplifying 2r2 + -9r + -8 = 0 Reorder the terms: -8 + -9r + 2r2 = 0 Solving -8 + -9r + 2r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -4.5r + r2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4.5r + 4 + r2 = 0 + 4 Reorder the terms: -4 + 4 + -4.5r + r2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4.5r + r2 = 0 + 4 -4.5r + r2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4.5r + r2 = 4 The r term is -4.5r. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5r + 5.0625 + r2 = 4 + 5.0625 Reorder the terms: 5.0625 + -4.5r + r2 = 4 + 5.0625 Combine like terms: 4 + 5.0625 = 9.0625 5.0625 + -4.5r + r2 = 9.0625 Factor a perfect square on the left side: (r + -2.25)(r + -2.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (r + -2.25) equal to 3.010398645 and -3.010398645.Subproblem 1
r + -2.25 = 3.010398645 Simplifying r + -2.25 = 3.010398645 Reorder the terms: -2.25 + r = 3.010398645 Solving -2.25 + r = 3.010398645 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + r = 3.010398645 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + r = 3.010398645 + 2.25 r = 3.010398645 + 2.25 Combine like terms: 3.010398645 + 2.25 = 5.260398645 r = 5.260398645 Simplifying r = 5.260398645Subproblem 2
r + -2.25 = -3.010398645 Simplifying r + -2.25 = -3.010398645 Reorder the terms: -2.25 + r = -3.010398645 Solving -2.25 + r = -3.010398645 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + r = -3.010398645 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + r = -3.010398645 + 2.25 r = -3.010398645 + 2.25 Combine like terms: -3.010398645 + 2.25 = -0.760398645 r = -0.760398645 Simplifying r = -0.760398645Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.260398645, -0.760398645}
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