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Simplifying r2 + -30r = 41 Reorder the terms: -30r + r2 = 41 Solving -30r + r2 = 41 Solving for variable 'r'. Reorder the terms: -41 + -30r + r2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + -30r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -30r + 41 + r2 = 0 + 41 Reorder the terms: -41 + 41 + -30r + r2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -30r + r2 = 0 + 41 -30r + r2 = 0 + 41 Combine like terms: 0 + 41 = 41 -30r + r2 = 41 The r term is -30r. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30r + 225 + r2 = 41 + 225 Reorder the terms: 225 + -30r + r2 = 41 + 225 Combine like terms: 41 + 225 = 266 225 + -30r + r2 = 266 Factor a perfect square on the left side: (r + -15)(r + -15) = 266 Calculate the square root of the right side: 16.30950643 Break this problem into two subproblems by setting (r + -15) equal to 16.30950643 and -16.30950643.Subproblem 1
r + -15 = 16.30950643 Simplifying r + -15 = 16.30950643 Reorder the terms: -15 + r = 16.30950643 Solving -15 + r = 16.30950643 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = 16.30950643 + 15 Combine like terms: -15 + 15 = 0 0 + r = 16.30950643 + 15 r = 16.30950643 + 15 Combine like terms: 16.30950643 + 15 = 31.30950643 r = 31.30950643 Simplifying r = 31.30950643Subproblem 2
r + -15 = -16.30950643 Simplifying r + -15 = -16.30950643 Reorder the terms: -15 + r = -16.30950643 Solving -15 + r = -16.30950643 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + r = -16.30950643 + 15 Combine like terms: -15 + 15 = 0 0 + r = -16.30950643 + 15 r = -16.30950643 + 15 Combine like terms: -16.30950643 + 15 = -1.30950643 r = -1.30950643 Simplifying r = -1.30950643Solution
The solution to the problem is based on the solutions from the subproblems. r = {31.30950643, -1.30950643}
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