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Simplifying 7r2 + 8r + -4 = 0 Reorder the terms: -4 + 8r + 7r2 = 0 Solving -4 + 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'. -0.5714285714 + 1.142857143r + r2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 1.142857143r + 0.5714285714 + r2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 1.142857143r + r2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 1.142857143r + r2 = 0 + 0.5714285714 1.142857143r + r2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 1.142857143r + r2 = 0.5714285714 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 = 0.5714285714 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143r + r2 = 0.5714285714 + 0.3265306123 Combine like terms: 0.5714285714 + 0.3265306123 = 0.8979591837 0.3265306123 + 1.142857143r + r2 = 0.8979591837 Factor a perfect square on the left side: (r + 0.5714285715)(r + 0.5714285715) = 0.8979591837 Calculate the square root of the right side: 0.947607083 Break this problem into two subproblems by setting (r + 0.5714285715) equal to 0.947607083 and -0.947607083.Subproblem 1
r + 0.5714285715 = 0.947607083 Simplifying r + 0.5714285715 = 0.947607083 Reorder the terms: 0.5714285715 + r = 0.947607083 Solving 0.5714285715 + r = 0.947607083 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 = 0.947607083 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + r = 0.947607083 + -0.5714285715 r = 0.947607083 + -0.5714285715 Combine like terms: 0.947607083 + -0.5714285715 = 0.3761785115 r = 0.3761785115 Simplifying r = 0.3761785115Subproblem 2
r + 0.5714285715 = -0.947607083 Simplifying r + 0.5714285715 = -0.947607083 Reorder the terms: 0.5714285715 + r = -0.947607083 Solving 0.5714285715 + r = -0.947607083 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 = -0.947607083 + -0.5714285715 Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000 0.0000000000 + r = -0.947607083 + -0.5714285715 r = -0.947607083 + -0.5714285715 Combine like terms: -0.947607083 + -0.5714285715 = -1.5190356545 r = -1.5190356545 Simplifying r = -1.5190356545Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.3761785115, -1.5190356545}
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