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Simplifying 9r2 + -18r + -69 = 4 Reorder the terms: -69 + -18r + 9r2 = 4 Solving -69 + -18r + 9r2 = 4 Solving for variable 'r'. Reorder the terms: -69 + -4 + -18r + 9r2 = 4 + -4 Combine like terms: -69 + -4 = -73 -73 + -18r + 9r2 = 4 + -4 Combine like terms: 4 + -4 = 0 -73 + -18r + 9r2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.111111111 + -2r + r2 = 0 Move the constant term to the right: Add '8.111111111' to each side of the equation. -8.111111111 + -2r + 8.111111111 + r2 = 0 + 8.111111111 Reorder the terms: -8.111111111 + 8.111111111 + -2r + r2 = 0 + 8.111111111 Combine like terms: -8.111111111 + 8.111111111 = 0.000000000 0.000000000 + -2r + r2 = 0 + 8.111111111 -2r + r2 = 0 + 8.111111111 Combine like terms: 0 + 8.111111111 = 8.111111111 -2r + r2 = 8.111111111 The r term is -2r. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r + 1 + r2 = 8.111111111 + 1 Reorder the terms: 1 + -2r + r2 = 8.111111111 + 1 Combine like terms: 8.111111111 + 1 = 9.111111111 1 + -2r + r2 = 9.111111111 Factor a perfect square on the left side: (r + -1)(r + -1) = 9.111111111 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (r + -1) equal to 3.018461713 and -3.018461713.Subproblem 1
r + -1 = 3.018461713 Simplifying r + -1 = 3.018461713 Reorder the terms: -1 + r = 3.018461713 Solving -1 + r = 3.018461713 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 3.018461713 + 1 Combine like terms: -1 + 1 = 0 0 + r = 3.018461713 + 1 r = 3.018461713 + 1 Combine like terms: 3.018461713 + 1 = 4.018461713 r = 4.018461713 Simplifying r = 4.018461713Subproblem 2
r + -1 = -3.018461713 Simplifying r + -1 = -3.018461713 Reorder the terms: -1 + r = -3.018461713 Solving -1 + r = -3.018461713 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -3.018461713 + 1 Combine like terms: -1 + 1 = 0 0 + r = -3.018461713 + 1 r = -3.018461713 + 1 Combine like terms: -3.018461713 + 1 = -2.018461713 r = -2.018461713 Simplifying r = -2.018461713Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.018461713, -2.018461713}
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