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Simplifying 4r2 + r + 8 = 0 Reorder the terms: 8 + r + 4r2 = 0 Solving 8 + r + 4r2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2 + 0.25r + r2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.25r + -2 + r2 = 0 + -2 Reorder the terms: 2 + -2 + 0.25r + r2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.25r + r2 = 0 + -2 0.25r + r2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.25r + r2 = -2 The r term is r. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25r + 0.25 + r2 = -2 + 0.25 Reorder the terms: 0.25 + 0.25r + r2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + 0.25r + r2 = -1.75 Factor a perfect square on the left side: (r + 0.5)(r + 0.5) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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