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Simplifying 7(r + -5) * r = 2 Reorder the terms: 7(-5 + r) * r = 2 Reorder the terms for easier multiplication: 7r(-5 + r) = 2 (-5 * 7r + r * 7r) = 2 (-35r + 7r2) = 2 Solving -35r + 7r2 = 2 Solving for variable 'r'. Reorder the terms: -2 + -35r + 7r2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -35r + 7r2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -5r + r2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -5r + 0.2857142857 + r2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -5r + r2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -5r + r2 = 0 + 0.2857142857 -5r + r2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -5r + r2 = 0.2857142857 The r term is -5r. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5r + 6.25 + r2 = 0.2857142857 + 6.25 Reorder the terms: 6.25 + -5r + r2 = 0.2857142857 + 6.25 Combine like terms: 0.2857142857 + 6.25 = 6.5357142857 6.25 + -5r + r2 = 6.5357142857 Factor a perfect square on the left side: (r + -2.5)(r + -2.5) = 6.5357142857 Calculate the square root of the right side: 2.55650431 Break this problem into two subproblems by setting (r + -2.5) equal to 2.55650431 and -2.55650431.Subproblem 1
r + -2.5 = 2.55650431 Simplifying r + -2.5 = 2.55650431 Reorder the terms: -2.5 + r = 2.55650431 Solving -2.5 + r = 2.55650431 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = 2.55650431 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = 2.55650431 + 2.5 r = 2.55650431 + 2.5 Combine like terms: 2.55650431 + 2.5 = 5.05650431 r = 5.05650431 Simplifying r = 5.05650431Subproblem 2
r + -2.5 = -2.55650431 Simplifying r + -2.5 = -2.55650431 Reorder the terms: -2.5 + r = -2.55650431 Solving -2.5 + r = -2.55650431 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + r = -2.55650431 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + r = -2.55650431 + 2.5 r = -2.55650431 + 2.5 Combine like terms: -2.55650431 + 2.5 = -0.05650431 r = -0.05650431 Simplifying r = -0.05650431Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.05650431, -0.05650431}
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