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Simplifying 7r2 = 70r + -174 Reorder the terms: 7r2 = -174 + 70r Solving 7r2 = -174 + 70r Solving for variable 'r'. Reorder the terms: 174 + -70r + 7r2 = -174 + 70r + 174 + -70r Reorder the terms: 174 + -70r + 7r2 = -174 + 174 + 70r + -70r Combine like terms: -174 + 174 = 0 174 + -70r + 7r2 = 0 + 70r + -70r 174 + -70r + 7r2 = 70r + -70r Combine like terms: 70r + -70r = 0 174 + -70r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 24.85714286 + -10r + r2 = 0 Move the constant term to the right: Add '-24.85714286' to each side of the equation. 24.85714286 + -10r + -24.85714286 + r2 = 0 + -24.85714286 Reorder the terms: 24.85714286 + -24.85714286 + -10r + r2 = 0 + -24.85714286 Combine like terms: 24.85714286 + -24.85714286 = 0.00000000 0.00000000 + -10r + r2 = 0 + -24.85714286 -10r + r2 = 0 + -24.85714286 Combine like terms: 0 + -24.85714286 = -24.85714286 -10r + r2 = -24.85714286 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = -24.85714286 + 25 Reorder the terms: 25 + -10r + r2 = -24.85714286 + 25 Combine like terms: -24.85714286 + 25 = 0.14285714 25 + -10r + r2 = 0.14285714 Factor a perfect square on the left side: (r + -5)(r + -5) = 0.14285714 Calculate the square root of the right side: 0.377964469 Break this problem into two subproblems by setting (r + -5) equal to 0.377964469 and -0.377964469.Subproblem 1
r + -5 = 0.377964469 Simplifying r + -5 = 0.377964469 Reorder the terms: -5 + r = 0.377964469 Solving -5 + r = 0.377964469 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 0.377964469 + 5 Combine like terms: -5 + 5 = 0 0 + r = 0.377964469 + 5 r = 0.377964469 + 5 Combine like terms: 0.377964469 + 5 = 5.377964469 r = 5.377964469 Simplifying r = 5.377964469Subproblem 2
r + -5 = -0.377964469 Simplifying r + -5 = -0.377964469 Reorder the terms: -5 + r = -0.377964469 Solving -5 + r = -0.377964469 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -0.377964469 + 5 Combine like terms: -5 + 5 = 0 0 + r = -0.377964469 + 5 r = -0.377964469 + 5 Combine like terms: -0.377964469 + 5 = 4.622035531 r = 4.622035531 Simplifying r = 4.622035531Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.377964469, 4.622035531}
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