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Simplifying 12r2 + 3r + 5 = 0 Reorder the terms: 5 + 3r + 12r2 = 0 Solving 5 + 3r + 12r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + 0.25r + r2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + 0.25r + -0.4166666667 + r2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + 0.25r + r2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + 0.25r + r2 = 0 + -0.4166666667 0.25r + r2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 0.25r + r2 = -0.4166666667 The r term is 0.25r. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25r + 0.015625 + r2 = -0.4166666667 + 0.015625 Reorder the terms: 0.015625 + 0.25r + r2 = -0.4166666667 + 0.015625 Combine like terms: -0.4166666667 + 0.015625 = -0.4010416667 0.015625 + 0.25r + r2 = -0.4010416667 Factor a perfect square on the left side: (r + 0.125)(r + 0.125) = -0.4010416667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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