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Simplifying t2 + tr + 2r2 = 0 Reorder the terms: rt + 2r2 + t2 = 0 Solving rt + 2r2 + t2 = 0 Solving for variable 'r'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5rt + r2 + 0.5t2 = 0 Move the constant term to the right: Add '-1t2' to each side of the equation. 0.5rt + r2 + 0.5t2 + -1t2 = 0 + -1t2 Combine like terms: 0.5t2 + -1t2 = -0.5t2 0.5rt + r2 + -0.5t2 = 0 + -1t2 Remove the zero: 0.5rt + r2 + -0.5t2 = -1t2 The r term is rt. Take half its coefficient (0.5t). Square it (0.25t2) and add it to both sides. Add '0.25t2' to each side of the equation. 0.5rt + r2 + -0.5t2 + 0.25t2 = -1t2 + 0.25t2 Combine like terms: -0.5t2 + 0.25t2 = -0.25t2 0.5rt + r2 + -0.25t2 = -1t2 + 0.25t2 Combine like terms: -1t2 + 0.25t2 = -0.75t2 0.5rt + r2 + -0.25t2 = -0.75t2 Factor a perfect square on the left side: (r + 0.5t)(r + 0.5t) = -0.75t2 Can't calculate square root of the right side. The solution to this equation could not be determined.
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