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Simplifying r2 + 2r = -101 Reorder the terms: 2r + r2 = -101 Solving 2r + r2 = -101 Solving for variable 'r'. Reorder the terms: 101 + 2r + r2 = -101 + 101 Combine like terms: -101 + 101 = 0 101 + 2r + r2 = 0 Begin completing the square. Move the constant term to the right: Add '-101' to each side of the equation. 101 + 2r + -101 + r2 = 0 + -101 Reorder the terms: 101 + -101 + 2r + r2 = 0 + -101 Combine like terms: 101 + -101 = 0 0 + 2r + r2 = 0 + -101 2r + r2 = 0 + -101 Combine like terms: 0 + -101 = -101 2r + r2 = -101 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 = -101 + 1 Reorder the terms: 1 + 2r + r2 = -101 + 1 Combine like terms: -101 + 1 = -100 1 + 2r + r2 = -100 Factor a perfect square on the left side: (r + 1)(r + 1) = -100 Can't calculate square root of the right side. The solution to this equation could not be determined.
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