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Simplifying r2 + 10r + 22 = 0 Reorder the terms: 22 + 10r + r2 = 0 Solving 22 + 10r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 10r + -22 + r2 = 0 + -22 Reorder the terms: 22 + -22 + 10r + r2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 10r + r2 = 0 + -22 10r + r2 = 0 + -22 Combine like terms: 0 + -22 = -22 10r + r2 = -22 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 = -22 + 25 Reorder the terms: 25 + 10r + r2 = -22 + 25 Combine like terms: -22 + 25 = 3 25 + 10r + r2 = 3 Factor a perfect square on the left side: (r + 5)(r + 5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (r + 5) equal to 1.732050808 and -1.732050808.Subproblem 1
r + 5 = 1.732050808 Simplifying r + 5 = 1.732050808 Reorder the terms: 5 + r = 1.732050808 Solving 5 + r = 1.732050808 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 = 1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + r = 1.732050808 + -5 r = 1.732050808 + -5 Combine like terms: 1.732050808 + -5 = -3.267949192 r = -3.267949192 Simplifying r = -3.267949192Subproblem 2
r + 5 = -1.732050808 Simplifying r + 5 = -1.732050808 Reorder the terms: 5 + r = -1.732050808 Solving 5 + r = -1.732050808 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 = -1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + r = -1.732050808 + -5 r = -1.732050808 + -5 Combine like terms: -1.732050808 + -5 = -6.732050808 r = -6.732050808 Simplifying r = -6.732050808Solution
The solution to the problem is based on the solutions from the subproblems. r = {-3.267949192, -6.732050808}
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