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Simplifying 5(r + -4) * r = 9 Reorder the terms: 5(-4 + r) * r = 9 Reorder the terms for easier multiplication: 5r(-4 + r) = 9 (-4 * 5r + r * 5r) = 9 (-20r + 5r2) = 9 Solving -20r + 5r2 = 9 Solving for variable 'r'. Reorder the terms: -9 + -20r + 5r2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -20r + 5r2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + -4r + r2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -4r + 1.8 + r2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -4r + r2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -4r + r2 = 0 + 1.8 -4r + r2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -4r + r2 = 1.8 The r term is -4r. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4r + 4 + r2 = 1.8 + 4 Reorder the terms: 4 + -4r + r2 = 1.8 + 4 Combine like terms: 1.8 + 4 = 5.8 4 + -4r + r2 = 5.8 Factor a perfect square on the left side: (r + -2)(r + -2) = 5.8 Calculate the square root of the right side: 2.408318916 Break this problem into two subproblems by setting (r + -2) equal to 2.408318916 and -2.408318916.Subproblem 1
r + -2 = 2.408318916 Simplifying r + -2 = 2.408318916 Reorder the terms: -2 + r = 2.408318916 Solving -2 + r = 2.408318916 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = 2.408318916 + 2 Combine like terms: -2 + 2 = 0 0 + r = 2.408318916 + 2 r = 2.408318916 + 2 Combine like terms: 2.408318916 + 2 = 4.408318916 r = 4.408318916 Simplifying r = 4.408318916Subproblem 2
r + -2 = -2.408318916 Simplifying r + -2 = -2.408318916 Reorder the terms: -2 + r = -2.408318916 Solving -2 + r = -2.408318916 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + r = -2.408318916 + 2 Combine like terms: -2 + 2 = 0 0 + r = -2.408318916 + 2 r = -2.408318916 + 2 Combine like terms: -2.408318916 + 2 = -0.408318916 r = -0.408318916 Simplifying r = -0.408318916Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.408318916, -0.408318916}
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