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Simplifying -7r2 + 2r + 15 = 0 Reorder the terms: 15 + 2r + -7r2 = 0 Solving 15 + 2r + -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'. -2.142857143 + -0.2857142857r + r2 = 0 Move the constant term to the right: Add '2.142857143' to each side of the equation. -2.142857143 + -0.2857142857r + 2.142857143 + r2 = 0 + 2.142857143 Reorder the terms: -2.142857143 + 2.142857143 + -0.2857142857r + r2 = 0 + 2.142857143 Combine like terms: -2.142857143 + 2.142857143 = 0.000000000 0.000000000 + -0.2857142857r + r2 = 0 + 2.142857143 -0.2857142857r + r2 = 0 + 2.142857143 Combine like terms: 0 + 2.142857143 = 2.142857143 -0.2857142857r + r2 = 2.142857143 The r term is -0.2857142857r. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857r + 0.02040816328 + r2 = 2.142857143 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857r + r2 = 2.142857143 + 0.02040816328 Combine like terms: 2.142857143 + 0.02040816328 = 2.16326530628 0.02040816328 + -0.2857142857r + r2 = 2.16326530628 Factor a perfect square on the left side: (r + -0.1428571429)(r + -0.1428571429) = 2.16326530628 Calculate the square root of the right side: 1.470804306 Break this problem into two subproblems by setting (r + -0.1428571429) equal to 1.470804306 and -1.470804306.Subproblem 1
r + -0.1428571429 = 1.470804306 Simplifying r + -0.1428571429 = 1.470804306 Reorder the terms: -0.1428571429 + r = 1.470804306 Solving -0.1428571429 + r = 1.470804306 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + r = 1.470804306 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + r = 1.470804306 + 0.1428571429 r = 1.470804306 + 0.1428571429 Combine like terms: 1.470804306 + 0.1428571429 = 1.6136614489 r = 1.6136614489 Simplifying r = 1.6136614489Subproblem 2
r + -0.1428571429 = -1.470804306 Simplifying r + -0.1428571429 = -1.470804306 Reorder the terms: -0.1428571429 + r = -1.470804306 Solving -0.1428571429 + r = -1.470804306 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + r = -1.470804306 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + r = -1.470804306 + 0.1428571429 r = -1.470804306 + 0.1428571429 Combine like terms: -1.470804306 + 0.1428571429 = -1.3279471631 r = -1.3279471631 Simplifying r = -1.3279471631Solution
The solution to the problem is based on the solutions from the subproblems. r = {1.6136614489, -1.3279471631}
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