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Simplifying r2 + -10r = -1 Reorder the terms: -10r + r2 = -1 Solving -10r + r2 = -1 Solving for variable 'r'. Reorder the terms: 1 + -10r + r2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + -10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10r + -1 + r2 = 0 + -1 Reorder the terms: 1 + -1 + -10r + r2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10r + r2 = 0 + -1 -10r + r2 = 0 + -1 Combine like terms: 0 + -1 = -1 -10r + r2 = -1 The r term is -10r. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10r + 25 + r2 = -1 + 25 Reorder the terms: 25 + -10r + r2 = -1 + 25 Combine like terms: -1 + 25 = 24 25 + -10r + r2 = 24 Factor a perfect square on the left side: (r + -5)(r + -5) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (r + -5) equal to 4.898979486 and -4.898979486.Subproblem 1
r + -5 = 4.898979486 Simplifying r + -5 = 4.898979486 Reorder the terms: -5 + r = 4.898979486 Solving -5 + r = 4.898979486 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = 4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + r = 4.898979486 + 5 r = 4.898979486 + 5 Combine like terms: 4.898979486 + 5 = 9.898979486 r = 9.898979486 Simplifying r = 9.898979486Subproblem 2
r + -5 = -4.898979486 Simplifying r + -5 = -4.898979486 Reorder the terms: -5 + r = -4.898979486 Solving -5 + r = -4.898979486 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + r = -4.898979486 + 5 Combine like terms: -5 + 5 = 0 0 + r = -4.898979486 + 5 r = -4.898979486 + 5 Combine like terms: -4.898979486 + 5 = 0.101020514 r = 0.101020514 Simplifying r = 0.101020514Solution
The solution to the problem is based on the solutions from the subproblems. r = {9.898979486, 0.101020514}
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