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Simplifying 3r2 + 7r + 1 + 4r2 + -8r + -2 = 0 Reorder the terms: 1 + -2 + 7r + -8r + 3r2 + 4r2 = 0 Combine like terms: 1 + -2 = -1 -1 + 7r + -8r + 3r2 + 4r2 = 0 Combine like terms: 7r + -8r = -1r -1 + -1r + 3r2 + 4r2 = 0 Combine like terms: 3r2 + 4r2 = 7r2 -1 + -1r + 7r2 = 0 Solving -1 + -1r + 7r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.1428571429r + r2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.1428571429r + 0.1428571429 + r2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.1428571429r + r2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.1428571429r + r2 = 0 + 0.1428571429 -0.1428571429r + r2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.1428571429r + r2 = 0.1428571429 The r term is -0.1428571429r. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429r + 0.005102040819 + r2 = 0.1428571429 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429r + r2 = 0.1428571429 + 0.005102040819 Combine like terms: 0.1428571429 + 0.005102040819 = 0.147959183719 0.005102040819 + -0.1428571429r + r2 = 0.147959183719 Factor a perfect square on the left side: (r + -0.07142857145)(r + -0.07142857145) = 0.147959183719 Calculate the square root of the right side: 0.384654629 Break this problem into two subproblems by setting (r + -0.07142857145) equal to 0.384654629 and -0.384654629.Subproblem 1
r + -0.07142857145 = 0.384654629 Simplifying r + -0.07142857145 = 0.384654629 Reorder the terms: -0.07142857145 + r = 0.384654629 Solving -0.07142857145 + r = 0.384654629 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + r = 0.384654629 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + r = 0.384654629 + 0.07142857145 r = 0.384654629 + 0.07142857145 Combine like terms: 0.384654629 + 0.07142857145 = 0.45608320045 r = 0.45608320045 Simplifying r = 0.45608320045Subproblem 2
r + -0.07142857145 = -0.384654629 Simplifying r + -0.07142857145 = -0.384654629 Reorder the terms: -0.07142857145 + r = -0.384654629 Solving -0.07142857145 + r = -0.384654629 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + r = -0.384654629 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + r = -0.384654629 + 0.07142857145 r = -0.384654629 + 0.07142857145 Combine like terms: -0.384654629 + 0.07142857145 = -0.31322605755 r = -0.31322605755 Simplifying r = -0.31322605755Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.45608320045, -0.31322605755}
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