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Simplifying r2 + 2r + -290 = 0 Reorder the terms: -290 + 2r + r2 = 0 Solving -290 + 2r + r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '290' to each side of the equation. -290 + 2r + 290 + r2 = 0 + 290 Reorder the terms: -290 + 290 + 2r + r2 = 0 + 290 Combine like terms: -290 + 290 = 0 0 + 2r + r2 = 0 + 290 2r + r2 = 0 + 290 Combine like terms: 0 + 290 = 290 2r + r2 = 290 The r term is 2r. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2r + 1 + r2 = 290 + 1 Reorder the terms: 1 + 2r + r2 = 290 + 1 Combine like terms: 290 + 1 = 291 1 + 2r + r2 = 291 Factor a perfect square on the left side: (r + 1)(r + 1) = 291 Calculate the square root of the right side: 17.058722109 Break this problem into two subproblems by setting (r + 1) equal to 17.058722109 and -17.058722109.Subproblem 1
r + 1 = 17.058722109 Simplifying r + 1 = 17.058722109 Reorder the terms: 1 + r = 17.058722109 Solving 1 + r = 17.058722109 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 17.058722109 + -1 Combine like terms: 1 + -1 = 0 0 + r = 17.058722109 + -1 r = 17.058722109 + -1 Combine like terms: 17.058722109 + -1 = 16.058722109 r = 16.058722109 Simplifying r = 16.058722109Subproblem 2
r + 1 = -17.058722109 Simplifying r + 1 = -17.058722109 Reorder the terms: 1 + r = -17.058722109 Solving 1 + r = -17.058722109 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -17.058722109 + -1 Combine like terms: 1 + -1 = 0 0 + r = -17.058722109 + -1 r = -17.058722109 + -1 Combine like terms: -17.058722109 + -1 = -18.058722109 r = -18.058722109 Simplifying r = -18.058722109Solution
The solution to the problem is based on the solutions from the subproblems. r = {16.058722109, -18.058722109}
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