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Simplifying r2 + -10r + 25 = 12 Reorder the terms: 25 + -10r + r2 = 12 Solving 25 + -10r + r2 = 12 Solving for variable 'r'. Reorder the terms: 25 + -12 + -10r + r2 = 12 + -12 Combine like terms: 25 + -12 = 13 13 + -10r + r2 = 12 + -12 Combine like terms: 12 + -12 = 0 13 + -10r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + -10r + -13 + r2 = 0 + -13 Reorder the terms: 13 + -13 + -10r + r2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -10r + r2 = 0 + -13 -10r + r2 = 0 + -13 Combine like terms: 0 + -13 = -13 -10r + r2 = -13 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 = -13 + 25 Reorder the terms: 25 + -10r + r2 = -13 + 25 Combine like terms: -13 + 25 = 12 25 + -10r + r2 = 12 Factor a perfect square on the left side: (r + -5)(r + -5) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (r + -5) equal to 3.464101615 and -3.464101615.Subproblem 1
r + -5 = 3.464101615 Simplifying r + -5 = 3.464101615 Reorder the terms: -5 + r = 3.464101615 Solving -5 + r = 3.464101615 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 = 3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + r = 3.464101615 + 5 r = 3.464101615 + 5 Combine like terms: 3.464101615 + 5 = 8.464101615 r = 8.464101615 Simplifying r = 8.464101615Subproblem 2
r + -5 = -3.464101615 Simplifying r + -5 = -3.464101615 Reorder the terms: -5 + r = -3.464101615 Solving -5 + r = -3.464101615 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 = -3.464101615 + 5 Combine like terms: -5 + 5 = 0 0 + r = -3.464101615 + 5 r = -3.464101615 + 5 Combine like terms: -3.464101615 + 5 = 1.535898385 r = 1.535898385 Simplifying r = 1.535898385Solution
The solution to the problem is based on the solutions from the subproblems. r = {8.464101615, 1.535898385}
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