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Simplifying 7r2 = 70r + 75 Reorder the terms: 7r2 = 75 + 70r Solving 7r2 = 75 + 70r Solving for variable 'r'. Reorder the terms: -75 + -70r + 7r2 = 75 + 70r + -75 + -70r Reorder the terms: -75 + -70r + 7r2 = 75 + -75 + 70r + -70r Combine like terms: 75 + -75 = 0 -75 + -70r + 7r2 = 0 + 70r + -70r -75 + -70r + 7r2 = 70r + -70r Combine like terms: 70r + -70r = 0 -75 + -70r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -10.71428571 + -10r + r2 = 0 Move the constant term to the right: Add '10.71428571' to each side of the equation. -10.71428571 + -10r + 10.71428571 + r2 = 0 + 10.71428571 Reorder the terms: -10.71428571 + 10.71428571 + -10r + r2 = 0 + 10.71428571 Combine like terms: -10.71428571 + 10.71428571 = 0.00000000 0.00000000 + -10r + r2 = 0 + 10.71428571 -10r + r2 = 0 + 10.71428571 Combine like terms: 0 + 10.71428571 = 10.71428571 -10r + r2 = 10.71428571 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 = 10.71428571 + 25 Reorder the terms: 25 + -10r + r2 = 10.71428571 + 25 Combine like terms: 10.71428571 + 25 = 35.71428571 25 + -10r + r2 = 35.71428571 Factor a perfect square on the left side: (r + -5)(r + -5) = 35.71428571 Calculate the square root of the right side: 5.976143046 Break this problem into two subproblems by setting (r + -5) equal to 5.976143046 and -5.976143046.Subproblem 1
r + -5 = 5.976143046 Simplifying r + -5 = 5.976143046 Reorder the terms: -5 + r = 5.976143046 Solving -5 + r = 5.976143046 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 = 5.976143046 + 5 Combine like terms: -5 + 5 = 0 0 + r = 5.976143046 + 5 r = 5.976143046 + 5 Combine like terms: 5.976143046 + 5 = 10.976143046 r = 10.976143046 Simplifying r = 10.976143046Subproblem 2
r + -5 = -5.976143046 Simplifying r + -5 = -5.976143046 Reorder the terms: -5 + r = -5.976143046 Solving -5 + r = -5.976143046 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 = -5.976143046 + 5 Combine like terms: -5 + 5 = 0 0 + r = -5.976143046 + 5 r = -5.976143046 + 5 Combine like terms: -5.976143046 + 5 = -0.976143046 r = -0.976143046 Simplifying r = -0.976143046Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.976143046, -0.976143046}
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