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Simplifying 7r2 + -114r = -7 Reorder the terms: -114r + 7r2 = -7 Solving -114r + 7r2 = -7 Solving for variable 'r'. Reorder the terms: 7 + -114r + 7r2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -114r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1 + -16.28571429r + r2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -16.28571429r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + -16.28571429r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -16.28571429r + r2 = 0 + -1 -16.28571429r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 -16.28571429r + r2 = -1 The r term is -16.28571429r. Take half its coefficient (-8.142857145). Square it (66.30612248) and add it to both sides. Add '66.30612248' to each side of the equation. -16.28571429r + 66.30612248 + r2 = -1 + 66.30612248 Reorder the terms: 66.30612248 + -16.28571429r + r2 = -1 + 66.30612248 Combine like terms: -1 + 66.30612248 = 65.30612248 66.30612248 + -16.28571429r + r2 = 65.30612248 Factor a perfect square on the left side: (r + -8.142857145)(r + -8.142857145) = 65.30612248 Calculate the square root of the right side: 8.081220358 Break this problem into two subproblems by setting (r + -8.142857145) equal to 8.081220358 and -8.081220358.Subproblem 1
r + -8.142857145 = 8.081220358 Simplifying r + -8.142857145 = 8.081220358 Reorder the terms: -8.142857145 + r = 8.081220358 Solving -8.142857145 + r = 8.081220358 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8.142857145' to each side of the equation. -8.142857145 + 8.142857145 + r = 8.081220358 + 8.142857145 Combine like terms: -8.142857145 + 8.142857145 = 0.000000000 0.000000000 + r = 8.081220358 + 8.142857145 r = 8.081220358 + 8.142857145 Combine like terms: 8.081220358 + 8.142857145 = 16.224077503 r = 16.224077503 Simplifying r = 16.224077503Subproblem 2
r + -8.142857145 = -8.081220358 Simplifying r + -8.142857145 = -8.081220358 Reorder the terms: -8.142857145 + r = -8.081220358 Solving -8.142857145 + r = -8.081220358 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '8.142857145' to each side of the equation. -8.142857145 + 8.142857145 + r = -8.081220358 + 8.142857145 Combine like terms: -8.142857145 + 8.142857145 = 0.000000000 0.000000000 + r = -8.081220358 + 8.142857145 r = -8.081220358 + 8.142857145 Combine like terms: -8.081220358 + 8.142857145 = 0.061636787 r = 0.061636787 Simplifying r = 0.061636787Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.224077503, 0.061636787}
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