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Simplifying 14r2 + -2r + -70 = 0 Reorder the terms: -70 + -2r + 14r2 = 0 Solving -70 + -2r + 14r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + -1r + 7r2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -1r + 7r2)' equal to zero and attempt to solve: Simplifying -35 + -1r + 7r2 = 0 Solving -35 + -1r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5 + -0.1428571429r + r2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.1428571429r + 5 + r2 = 0 + 5 Reorder the terms: -5 + 5 + -0.1428571429r + r2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.1428571429r + r2 = 0 + 5 -0.1428571429r + r2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.1428571429r + r2 = 5 The r term is -0.1428571429r. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429r + 0.005102040819 + r2 = 5 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429r + r2 = 5 + 0.005102040819 Combine like terms: 5 + 0.005102040819 = 5.005102040819 0.005102040819 + -0.1428571429r + r2 = 5.005102040819 Factor a perfect square on the left side: (r + -0.07142857145)(r + -0.07142857145) = 5.005102040819 Calculate the square root of the right side: 2.237208538 Break this problem into two subproblems by setting (r + -0.07142857145) equal to 2.237208538 and -2.237208538.Subproblem 1
r + -0.07142857145 = 2.237208538 Simplifying r + -0.07142857145 = 2.237208538 Reorder the terms: -0.07142857145 + r = 2.237208538 Solving -0.07142857145 + r = 2.237208538 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + r = 2.237208538 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + r = 2.237208538 + 0.07142857145 r = 2.237208538 + 0.07142857145 Combine like terms: 2.237208538 + 0.07142857145 = 2.30863710945 r = 2.30863710945 Simplifying r = 2.30863710945Subproblem 2
r + -0.07142857145 = -2.237208538 Simplifying r + -0.07142857145 = -2.237208538 Reorder the terms: -0.07142857145 + r = -2.237208538 Solving -0.07142857145 + r = -2.237208538 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + r = -2.237208538 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + r = -2.237208538 + 0.07142857145 r = -2.237208538 + 0.07142857145 Combine like terms: -2.237208538 + 0.07142857145 = -2.16577996655 r = -2.16577996655 Simplifying r = -2.16577996655Solution
The solution to the problem is based on the solutions from the subproblems. r = {2.30863710945, -2.16577996655}Solution
r = {2.30863710945, -2.16577996655}
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