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Simplifying (1 + -1r)(1 + -1r) + 4 = 0 Multiply (1 + -1r) * (1 + -1r) (1(1 + -1r) + -1r * (1 + -1r)) + 4 = 0 ((1 * 1 + -1r * 1) + -1r * (1 + -1r)) + 4 = 0 ((1 + -1r) + -1r * (1 + -1r)) + 4 = 0 (1 + -1r + (1 * -1r + -1r * -1r)) + 4 = 0 (1 + -1r + (-1r + 1r2)) + 4 = 0 Combine like terms: -1r + -1r = -2r (1 + -2r + 1r2) + 4 = 0 Reorder the terms: 1 + 4 + -2r + 1r2 = 0 Combine like terms: 1 + 4 = 5 5 + -2r + 1r2 = 0 Solving 5 + -2r + 1r2 = 0 Solving for variable 'r'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -2r + -5 + r2 = 0 + -5 Reorder the terms: 5 + -5 + -2r + r2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r + r2 = 0 + -5 -2r + r2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2r + r2 = -5 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 = -5 + 1 Reorder the terms: 1 + -2r + r2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + -2r + r2 = -4 Factor a perfect square on the left side: (r + -1)(r + -1) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined.
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