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Simplifying r2 + -51 = 6r Reorder the terms: -51 + r2 = 6r Solving -51 + r2 = 6r Solving for variable 'r'. Reorder the terms: -51 + -6r + r2 = 6r + -6r Combine like terms: 6r + -6r = 0 -51 + -6r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -6r + 51 + r2 = 0 + 51 Reorder the terms: -51 + 51 + -6r + r2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -6r + r2 = 0 + 51 -6r + r2 = 0 + 51 Combine like terms: 0 + 51 = 51 -6r + r2 = 51 The r term is -6r. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6r + 9 + r2 = 51 + 9 Reorder the terms: 9 + -6r + r2 = 51 + 9 Combine like terms: 51 + 9 = 60 9 + -6r + r2 = 60 Factor a perfect square on the left side: (r + -3)(r + -3) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (r + -3) equal to 7.745966692 and -7.745966692.Subproblem 1
r + -3 = 7.745966692 Simplifying r + -3 = 7.745966692 Reorder the terms: -3 + r = 7.745966692 Solving -3 + r = 7.745966692 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = 7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + r = 7.745966692 + 3 r = 7.745966692 + 3 Combine like terms: 7.745966692 + 3 = 10.745966692 r = 10.745966692 Simplifying r = 10.745966692Subproblem 2
r + -3 = -7.745966692 Simplifying r + -3 = -7.745966692 Reorder the terms: -3 + r = -7.745966692 Solving -3 + r = -7.745966692 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + r = -7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + r = -7.745966692 + 3 r = -7.745966692 + 3 Combine like terms: -7.745966692 + 3 = -4.745966692 r = -4.745966692 Simplifying r = -4.745966692Solution
The solution to the problem is based on the solutions from the subproblems. r = {10.745966692, -4.745966692}
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