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Simplifying 7r2 + -14 = 10r Reorder the terms: -14 + 7r2 = 10r Solving -14 + 7r2 = 10r Solving for variable 'r'. Reorder the terms: -14 + -10r + 7r2 = 10r + -10r Combine like terms: 10r + -10r = 0 -14 + -10r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2 + -1.428571429r + r2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.428571429r + 2 + r2 = 0 + 2 Reorder the terms: -2 + 2 + -1.428571429r + r2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.428571429r + r2 = 0 + 2 -1.428571429r + r2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.428571429r + r2 = 2 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 = 2 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429r + r2 = 2 + 0.5102040819 Combine like terms: 2 + 0.5102040819 = 2.5102040819 0.5102040819 + -1.428571429r + r2 = 2.5102040819 Factor a perfect square on the left side: (r + -0.7142857145)(r + -0.7142857145) = 2.5102040819 Calculate the square root of the right side: 1.584362358 Break this problem into two subproblems by setting (r + -0.7142857145) equal to 1.584362358 and -1.584362358.Subproblem 1
r + -0.7142857145 = 1.584362358 Simplifying r + -0.7142857145 = 1.584362358 Reorder the terms: -0.7142857145 + r = 1.584362358 Solving -0.7142857145 + r = 1.584362358 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 = 1.584362358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + r = 1.584362358 + 0.7142857145 r = 1.584362358 + 0.7142857145 Combine like terms: 1.584362358 + 0.7142857145 = 2.2986480725 r = 2.2986480725 Simplifying r = 2.2986480725Subproblem 2
r + -0.7142857145 = -1.584362358 Simplifying r + -0.7142857145 = -1.584362358 Reorder the terms: -0.7142857145 + r = -1.584362358 Solving -0.7142857145 + r = -1.584362358 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 = -1.584362358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + r = -1.584362358 + 0.7142857145 r = -1.584362358 + 0.7142857145 Combine like terms: -1.584362358 + 0.7142857145 = -0.8700766435 r = -0.8700766435 Simplifying r = -0.8700766435Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.2986480725, -0.8700766435}
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