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Simplifying r2 + -2r + -69 = 7 Reorder the terms: -69 + -2r + r2 = 7 Solving -69 + -2r + r2 = 7 Solving for variable 'r'. Reorder the terms: -69 + -7 + -2r + r2 = 7 + -7 Combine like terms: -69 + -7 = -76 -76 + -2r + r2 = 7 + -7 Combine like terms: 7 + -7 = 0 -76 + -2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + -2r + 76 + r2 = 0 + 76 Reorder the terms: -76 + 76 + -2r + r2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + -2r + r2 = 0 + 76 -2r + r2 = 0 + 76 Combine like terms: 0 + 76 = 76 -2r + r2 = 76 The r term is -2r. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2r + 1 + r2 = 76 + 1 Reorder the terms: 1 + -2r + r2 = 76 + 1 Combine like terms: 76 + 1 = 77 1 + -2r + r2 = 77 Factor a perfect square on the left side: (r + -1)(r + -1) = 77 Calculate the square root of the right side: 8.774964387 Break this problem into two subproblems by setting (r + -1) equal to 8.774964387 and -8.774964387.Subproblem 1
r + -1 = 8.774964387 Simplifying r + -1 = 8.774964387 Reorder the terms: -1 + r = 8.774964387 Solving -1 + r = 8.774964387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = 8.774964387 + 1 Combine like terms: -1 + 1 = 0 0 + r = 8.774964387 + 1 r = 8.774964387 + 1 Combine like terms: 8.774964387 + 1 = 9.774964387 r = 9.774964387 Simplifying r = 9.774964387Subproblem 2
r + -1 = -8.774964387 Simplifying r + -1 = -8.774964387 Reorder the terms: -1 + r = -8.774964387 Solving -1 + r = -8.774964387 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + r = -8.774964387 + 1 Combine like terms: -1 + 1 = 0 0 + r = -8.774964387 + 1 r = -8.774964387 + 1 Combine like terms: -8.774964387 + 1 = -7.774964387 r = -7.774964387 Simplifying r = -7.774964387Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.774964387, -7.774964387}
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