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Simplifying r2 + -10r + -27 = 0 Reorder the terms: -27 + -10r + r2 = 0 Solving -27 + -10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -10r + 27 + r2 = 0 + 27 Reorder the terms: -27 + 27 + -10r + r2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -10r + r2 = 0 + 27 -10r + r2 = 0 + 27 Combine like terms: 0 + 27 = 27 -10r + r2 = 27 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 = 27 + 25 Reorder the terms: 25 + -10r + r2 = 27 + 25 Combine like terms: 27 + 25 = 52 25 + -10r + r2 = 52 Factor a perfect square on the left side: (r + -5)(r + -5) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (r + -5) equal to 7.211102551 and -7.211102551.Subproblem 1
r + -5 = 7.211102551 Simplifying r + -5 = 7.211102551 Reorder the terms: -5 + r = 7.211102551 Solving -5 + r = 7.211102551 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 = 7.211102551 + 5 Combine like terms: -5 + 5 = 0 0 + r = 7.211102551 + 5 r = 7.211102551 + 5 Combine like terms: 7.211102551 + 5 = 12.211102551 r = 12.211102551 Simplifying r = 12.211102551Subproblem 2
r + -5 = -7.211102551 Simplifying r + -5 = -7.211102551 Reorder the terms: -5 + r = -7.211102551 Solving -5 + r = -7.211102551 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 = -7.211102551 + 5 Combine like terms: -5 + 5 = 0 0 + r = -7.211102551 + 5 r = -7.211102551 + 5 Combine like terms: -7.211102551 + 5 = -2.211102551 r = -2.211102551 Simplifying r = -2.211102551Solution
The solution to the problem is based on the solutions from the subproblems. r = {12.211102551, -2.211102551}
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