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Simplifying 5r2 + -14r + 109 = 0 Reorder the terms: 109 + -14r + 5r2 = 0 Solving 109 + -14r + 5r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 21.8 + -2.8r + r2 = 0 Move the constant term to the right: Add '-21.8' to each side of the equation. 21.8 + -2.8r + -21.8 + r2 = 0 + -21.8 Reorder the terms: 21.8 + -21.8 + -2.8r + r2 = 0 + -21.8 Combine like terms: 21.8 + -21.8 = 0.0 0.0 + -2.8r + r2 = 0 + -21.8 -2.8r + r2 = 0 + -21.8 Combine like terms: 0 + -21.8 = -21.8 -2.8r + r2 = -21.8 The r term is -2.8r. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8r + 1.96 + r2 = -21.8 + 1.96 Reorder the terms: 1.96 + -2.8r + r2 = -21.8 + 1.96 Combine like terms: -21.8 + 1.96 = -19.84 1.96 + -2.8r + r2 = -19.84 Factor a perfect square on the left side: (r + -1.4)(r + -1.4) = -19.84 Can't calculate square root of the right side. The solution to this equation could not be determined.
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