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Simplifying 7r2 + -20 = -8r Reorder the terms: -20 + 7r2 = -8r Solving -20 + 7r2 = -8r Solving for variable 'r'. Reorder the terms: -20 + 8r + 7r2 = -8r + 8r Combine like terms: -8r + 8r = 0 -20 + 8r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.857142857 + 1.142857143r + r2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 1.142857143r + 2.857142857 + r2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 1.142857143r + r2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 1.142857143r + r2 = 0 + 2.857142857 1.142857143r + r2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 1.142857143r + r2 = 2.857142857 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 = 2.857142857 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143r + r2 = 2.857142857 + 0.3265306123 Combine like terms: 2.857142857 + 0.3265306123 = 3.1836734693 0.3265306123 + 1.142857143r + r2 = 3.1836734693 Factor a perfect square on the left side: (r + 0.5714285715)(r + 0.5714285715) = 3.1836734693 Calculate the square root of the right side: 1.784285142 Break this problem into two subproblems by setting (r + 0.5714285715) equal to 1.784285142 and -1.784285142.Subproblem 1
r + 0.5714285715 = 1.784285142 Simplifying r + 0.5714285715 = 1.784285142 Reorder the terms: 0.5714285715 + r = 1.784285142 Solving 0.5714285715 + r = 1.784285142 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 = 1.784285142 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + r = 1.784285142 + -0.5714285715 r = 1.784285142 + -0.5714285715 Combine like terms: 1.784285142 + -0.5714285715 = 1.2128565705 r = 1.2128565705 Simplifying r = 1.2128565705Subproblem 2
r + 0.5714285715 = -1.784285142 Simplifying r + 0.5714285715 = -1.784285142 Reorder the terms: 0.5714285715 + r = -1.784285142 Solving 0.5714285715 + r = -1.784285142 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 = -1.784285142 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + r = -1.784285142 + -0.5714285715 r = -1.784285142 + -0.5714285715 Combine like terms: -1.784285142 + -0.5714285715 = -2.3557137135 r = -2.3557137135 Simplifying r = -2.3557137135Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.2128565705, -2.3557137135}
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