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Simplifying -7r2 + -10r + 3 = 0 Reorder the terms: 3 + -10r + -7r2 = 0 Solving 3 + -10r + -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'. -0.4285714286 + 1.428571429r + r2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 1.428571429r + 0.4285714286 + r2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 1.428571429r + r2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 1.428571429r + r2 = 0 + 0.4285714286 1.428571429r + r2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 1.428571429r + r2 = 0.4285714286 The r term is 1.428571429r. Take half its coefficient (0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. 1.428571429r + 0.5102040819 + r2 = 0.4285714286 + 0.5102040819 Reorder the terms: 0.5102040819 + 1.428571429r + r2 = 0.4285714286 + 0.5102040819 Combine like terms: 0.4285714286 + 0.5102040819 = 0.9387755105 0.5102040819 + 1.428571429r + r2 = 0.9387755105 Factor a perfect square on the left side: (r + 0.7142857145)(r + 0.7142857145) = 0.9387755105 Calculate the square root of the right side: 0.968904283 Break this problem into two subproblems by setting (r + 0.7142857145) equal to 0.968904283 and -0.968904283.Subproblem 1
r + 0.7142857145 = 0.968904283 Simplifying r + 0.7142857145 = 0.968904283 Reorder the terms: 0.7142857145 + r = 0.968904283 Solving 0.7142857145 + r = 0.968904283 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + r = 0.968904283 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + r = 0.968904283 + -0.7142857145 r = 0.968904283 + -0.7142857145 Combine like terms: 0.968904283 + -0.7142857145 = 0.2546185685 r = 0.2546185685 Simplifying r = 0.2546185685Subproblem 2
r + 0.7142857145 = -0.968904283 Simplifying r + 0.7142857145 = -0.968904283 Reorder the terms: 0.7142857145 + r = -0.968904283 Solving 0.7142857145 + r = -0.968904283 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + r = -0.968904283 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + r = -0.968904283 + -0.7142857145 r = -0.968904283 + -0.7142857145 Combine like terms: -0.968904283 + -0.7142857145 = -1.6831899975 r = -1.6831899975 Simplifying r = -1.6831899975Solution
The solution to the problem is based on the solutions from the subproblems. r = {0.2546185685, -1.6831899975}
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