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Simplifying t = 2 + -2[2t + -3](1 + -1t) Reorder the terms: t = 2 + -2[-3 + 2t](1 + -1t) Multiply [-3 + 2t] * (1 + -1t) t = 2 + -2[-3(1 + -1t) + 2t * (1 + -1t)] t = 2 + -2[(1 * -3 + -1t * -3) + 2t * (1 + -1t)] t = 2 + -2[(-3 + 3t) + 2t * (1 + -1t)] t = 2 + -2[-3 + 3t + (1 * 2t + -1t * 2t)] t = 2 + -2[-3 + 3t + (2t + -2t2)] Combine like terms: 3t + 2t = 5t t = 2 + -2[-3 + 5t + -2t2] t = 2 + [-3 * -2 + 5t * -2 + -2t2 * -2] t = 2 + [6 + -10t + 4t2] Combine like terms: 2 + 6 = 8 t = 8 + -10t + 4t2 Solving t = 8 + -10t + 4t2 Solving for variable 't'. Reorder the terms: -8 + t + 10t + -4t2 = 8 + -10t + 4t2 + -8 + 10t + -4t2 Combine like terms: t + 10t = 11t -8 + 11t + -4t2 = 8 + -10t + 4t2 + -8 + 10t + -4t2 Reorder the terms: -8 + 11t + -4t2 = 8 + -8 + -10t + 10t + 4t2 + -4t2 Combine like terms: 8 + -8 = 0 -8 + 11t + -4t2 = 0 + -10t + 10t + 4t2 + -4t2 -8 + 11t + -4t2 = -10t + 10t + 4t2 + -4t2 Combine like terms: -10t + 10t = 0 -8 + 11t + -4t2 = 0 + 4t2 + -4t2 -8 + 11t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -8 + 11t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2 + -2.75t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.75t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -2.75t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.75t + t2 = 0 + -2 -2.75t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.75t + t2 = -2 The t term is -2.75t. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75t + 1.890625 + t2 = -2 + 1.890625 Reorder the terms: 1.890625 + -2.75t + t2 = -2 + 1.890625 Combine like terms: -2 + 1.890625 = -0.109375 1.890625 + -2.75t + t2 = -0.109375 Factor a perfect square on the left side: (t + -1.375)(t + -1.375) = -0.109375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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