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Simplifying 2.5 = 4.9t2 + -2t Reorder the terms: 2.5 = -2t + 4.9t2 Solving 2.5 = -2t + 4.9t2 Solving for variable 't'. Reorder the terms: 2.5 + 2t + -4.9t2 = -2t + 2t + 4.9t2 + -4.9t2 Combine like terms: -2t + 2t = 0 2.5 + 2t + -4.9t2 = 0 + 4.9t2 + -4.9t2 2.5 + 2t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 2.5 + 2t + -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 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + -0.4081632653t + 0.5102040816 + t2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + -0.4081632653t + t2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + -0.4081632653t + t2 = 0 + 0.5102040816 -0.4081632653t + t2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 -0.4081632653t + t2 = 0.5102040816 The t term is -0.4081632653t. Take half its coefficient (-0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. -0.4081632653t + 0.04164931281 + t2 = 0.5102040816 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = 0.5102040816 + 0.04164931281 Combine like terms: 0.5102040816 + 0.04164931281 = 0.55185339441 0.04164931281 + -0.4081632653t + t2 = 0.55185339441 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 0.55185339441 Calculate the square root of the right side: 0.742868356 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 0.742868356 and -0.742868356.Subproblem 1
t + -0.2040816327 = 0.742868356 Simplifying t + -0.2040816327 = 0.742868356 Reorder the terms: -0.2040816327 + t = 0.742868356 Solving -0.2040816327 + t = 0.742868356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = 0.742868356 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 0.742868356 + 0.2040816327 t = 0.742868356 + 0.2040816327 Combine like terms: 0.742868356 + 0.2040816327 = 0.9469499887 t = 0.9469499887 Simplifying t = 0.9469499887Subproblem 2
t + -0.2040816327 = -0.742868356 Simplifying t + -0.2040816327 = -0.742868356 Reorder the terms: -0.2040816327 + t = -0.742868356 Solving -0.2040816327 + t = -0.742868356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = -0.742868356 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -0.742868356 + 0.2040816327 t = -0.742868356 + 0.2040816327 Combine like terms: -0.742868356 + 0.2040816327 = -0.5387867233 t = -0.5387867233 Simplifying t = -0.5387867233Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.9469499887, -0.5387867233}
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