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Simplifying -4.9t2 + 10t + 2 = 4.5 Reorder the terms: 2 + 10t + -4.9t2 = 4.5 Solving 2 + 10t + -4.9t2 = 4.5 Solving for variable 't'. Reorder the terms: 2 + -4.5 + 10t + -4.9t2 = 4.5 + -4.5 Combine like terms: 2 + -4.5 = -2.5 -2.5 + 10t + -4.9t2 = 4.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 -2.5 + 10t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. 0.5102040816 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '-0.5102040816' to each side of the equation. 0.5102040816 + -2.040816327t + -0.5102040816 + t2 = 0 + -0.5102040816 Reorder the terms: 0.5102040816 + -0.5102040816 + -2.040816327t + t2 = 0 + -0.5102040816 Combine like terms: 0.5102040816 + -0.5102040816 = 0.0000000000 0.0000000000 + -2.040816327t + t2 = 0 + -0.5102040816 -2.040816327t + t2 = 0 + -0.5102040816 Combine like terms: 0 + -0.5102040816 = -0.5102040816 -2.040816327t + t2 = -0.5102040816 The t term is -2.040816327t. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327t + 1.041232821 + t2 = -0.5102040816 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = -0.5102040816 + 1.041232821 Combine like terms: -0.5102040816 + 1.041232821 = 0.5310287394 1.041232821 + -2.040816327t + t2 = 0.5310287394 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 0.5310287394 Calculate the square root of the right side: 0.728717188 Break this problem into two subproblems by setting (t + -1.020408164) equal to 0.728717188 and -0.728717188.Subproblem 1
t + -1.020408164 = 0.728717188 Simplifying t + -1.020408164 = 0.728717188 Reorder the terms: -1.020408164 + t = 0.728717188 Solving -1.020408164 + t = 0.728717188 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 0.728717188 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 0.728717188 + 1.020408164 t = 0.728717188 + 1.020408164 Combine like terms: 0.728717188 + 1.020408164 = 1.749125352 t = 1.749125352 Simplifying t = 1.749125352Subproblem 2
t + -1.020408164 = -0.728717188 Simplifying t + -1.020408164 = -0.728717188 Reorder the terms: -1.020408164 + t = -0.728717188 Solving -1.020408164 + t = -0.728717188 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -0.728717188 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -0.728717188 + 1.020408164 t = -0.728717188 + 1.020408164 Combine like terms: -0.728717188 + 1.020408164 = 0.291690976 t = 0.291690976 Simplifying t = 0.291690976Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.749125352, 0.291690976}
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