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Simplifying 7r2 + -8r + -9 = 0 Reorder the terms: -9 + -8r + 7r2 = 0 Solving -9 + -8r + 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'. -1.285714286 + -1.142857143r + r2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -1.142857143r + 1.285714286 + r2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -1.142857143r + r2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -1.142857143r + r2 = 0 + 1.285714286 -1.142857143r + r2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -1.142857143r + r2 = 1.285714286 The r term is -1.142857143r. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143r + 0.3265306123 + r2 = 1.285714286 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143r + r2 = 1.285714286 + 0.3265306123 Combine like terms: 1.285714286 + 0.3265306123 = 1.6122448983 0.3265306123 + -1.142857143r + r2 = 1.6122448983 Factor a perfect square on the left side: (r + -0.5714285715)(r + -0.5714285715) = 1.6122448983 Calculate the square root of the right side: 1.26974206 Break this problem into two subproblems by setting (r + -0.5714285715) equal to 1.26974206 and -1.26974206.Subproblem 1
r + -0.5714285715 = 1.26974206 Simplifying r + -0.5714285715 = 1.26974206 Reorder the terms: -0.5714285715 + r = 1.26974206 Solving -0.5714285715 + r = 1.26974206 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + r = 1.26974206 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + r = 1.26974206 + 0.5714285715 r = 1.26974206 + 0.5714285715 Combine like terms: 1.26974206 + 0.5714285715 = 1.8411706315 r = 1.8411706315 Simplifying r = 1.8411706315Subproblem 2
r + -0.5714285715 = -1.26974206 Simplifying r + -0.5714285715 = -1.26974206 Reorder the terms: -0.5714285715 + r = -1.26974206 Solving -0.5714285715 + r = -1.26974206 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + r = -1.26974206 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + r = -1.26974206 + 0.5714285715 r = -1.26974206 + 0.5714285715 Combine like terms: -1.26974206 + 0.5714285715 = -0.6983134885 r = -0.6983134885 Simplifying r = -0.6983134885Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.8411706315, -0.6983134885}
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