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Simplifying 3r2 + 5r + 12 = 0 Reorder the terms: 12 + 5r + 3r2 = 0 Solving 12 + 5r + 3r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 1.666666667r + r2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 1.666666667r + -4 + r2 = 0 + -4 Reorder the terms: 4 + -4 + 1.666666667r + r2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 1.666666667r + r2 = 0 + -4 1.666666667r + r2 = 0 + -4 Combine like terms: 0 + -4 = -4 1.666666667r + r2 = -4 The r term is 1.666666667r. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667r + 0.6944444447 + r2 = -4 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667r + r2 = -4 + 0.6944444447 Combine like terms: -4 + 0.6944444447 = -3.3055555553 0.6944444447 + 1.666666667r + r2 = -3.3055555553 Factor a perfect square on the left side: (r + 0.8333333335)(r + 0.8333333335) = -3.3055555553 Can't calculate square root of the right side. The solution to this equation could not be determined.
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