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Simplifying r2 + 4r = 56 Reorder the terms: 4r + r2 = 56 Solving 4r + r2 = 56 Solving for variable 'r'. Reorder the terms: -56 + 4r + r2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 4r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 4r + 56 + r2 = 0 + 56 Reorder the terms: -56 + 56 + 4r + r2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 4r + r2 = 0 + 56 4r + r2 = 0 + 56 Combine like terms: 0 + 56 = 56 4r + r2 = 56 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 = 56 + 4 Reorder the terms: 4 + 4r + r2 = 56 + 4 Combine like terms: 56 + 4 = 60 4 + 4r + r2 = 60 Factor a perfect square on the left side: (r + 2)(r + 2) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (r + 2) equal to 7.745966692 and -7.745966692.Subproblem 1
r + 2 = 7.745966692 Simplifying r + 2 = 7.745966692 Reorder the terms: 2 + r = 7.745966692 Solving 2 + r = 7.745966692 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 = 7.745966692 + -2 Combine like terms: 2 + -2 = 0 0 + r = 7.745966692 + -2 r = 7.745966692 + -2 Combine like terms: 7.745966692 + -2 = 5.745966692 r = 5.745966692 Simplifying r = 5.745966692Subproblem 2
r + 2 = -7.745966692 Simplifying r + 2 = -7.745966692 Reorder the terms: 2 + r = -7.745966692 Solving 2 + r = -7.745966692 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 = -7.745966692 + -2 Combine like terms: 2 + -2 = 0 0 + r = -7.745966692 + -2 r = -7.745966692 + -2 Combine like terms: -7.745966692 + -2 = -9.745966692 r = -9.745966692 Simplifying r = -9.745966692Solution
The solution to the problem is based on the solutions from the subproblems. r = {5.745966692, -9.745966692}
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