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Simplifying 57r2 + -17r = 3 Reorder the terms: -17r + 57r2 = 3 Solving -17r + 57r2 = 3 Solving for variable 'r'. Reorder the terms: -3 + -17r + 57r2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -17r + 57r2 = 0 Begin completing the square. Divide all terms by 57 the coefficient of the squared term: Divide each side by '57'. -0.05263157895 + -0.298245614r + r2 = 0 Move the constant term to the right: Add '0.05263157895' to each side of the equation. -0.05263157895 + -0.298245614r + 0.05263157895 + r2 = 0 + 0.05263157895 Reorder the terms: -0.05263157895 + 0.05263157895 + -0.298245614r + r2 = 0 + 0.05263157895 Combine like terms: -0.05263157895 + 0.05263157895 = 0.00000000000 0.00000000000 + -0.298245614r + r2 = 0 + 0.05263157895 -0.298245614r + r2 = 0 + 0.05263157895 Combine like terms: 0 + 0.05263157895 = 0.05263157895 -0.298245614r + r2 = 0.05263157895 The r term is -0.298245614r. Take half its coefficient (-0.149122807). Square it (0.02223761157) and add it to both sides. Add '0.02223761157' to each side of the equation. -0.298245614r + 0.02223761157 + r2 = 0.05263157895 + 0.02223761157 Reorder the terms: 0.02223761157 + -0.298245614r + r2 = 0.05263157895 + 0.02223761157 Combine like terms: 0.05263157895 + 0.02223761157 = 0.07486919052 0.02223761157 + -0.298245614r + r2 = 0.07486919052 Factor a perfect square on the left side: (r + -0.149122807)(r + -0.149122807) = 0.07486919052 Calculate the square root of the right side: 0.27362235 Break this problem into two subproblems by setting (r + -0.149122807) equal to 0.27362235 and -0.27362235.Subproblem 1
r + -0.149122807 = 0.27362235 Simplifying r + -0.149122807 = 0.27362235 Reorder the terms: -0.149122807 + r = 0.27362235 Solving -0.149122807 + r = 0.27362235 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.149122807' to each side of the equation. -0.149122807 + 0.149122807 + r = 0.27362235 + 0.149122807 Combine like terms: -0.149122807 + 0.149122807 = 0.000000000 0.000000000 + r = 0.27362235 + 0.149122807 r = 0.27362235 + 0.149122807 Combine like terms: 0.27362235 + 0.149122807 = 0.422745157 r = 0.422745157 Simplifying r = 0.422745157Subproblem 2
r + -0.149122807 = -0.27362235 Simplifying r + -0.149122807 = -0.27362235 Reorder the terms: -0.149122807 + r = -0.27362235 Solving -0.149122807 + r = -0.27362235 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.149122807' to each side of the equation. -0.149122807 + 0.149122807 + r = -0.27362235 + 0.149122807 Combine like terms: -0.149122807 + 0.149122807 = 0.000000000 0.000000000 + r = -0.27362235 + 0.149122807 r = -0.27362235 + 0.149122807 Combine like terms: -0.27362235 + 0.149122807 = -0.124499543 r = -0.124499543 Simplifying r = -0.124499543Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.422745157, -0.124499543}
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