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Simplifying 0 = 2.5 + (3.46) * t + -4.9t2 Solving 0 = 2.5 + 3.46t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -2.5 = -2.5 -2.5 + -3.46t + 4.9t2 = 2.5 + 3.46t + -4.9t2 + -2.5 + -3.46t + 4.9t2 Reorder the terms: -2.5 + -3.46t + 4.9t2 = 2.5 + -2.5 + 3.46t + -3.46t + -4.9t2 + 4.9t2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + -3.46t + 4.9t2 = 0.0 + 3.46t + -3.46t + -4.9t2 + 4.9t2 -2.5 + -3.46t + 4.9t2 = 3.46t + -3.46t + -4.9t2 + 4.9t2 Combine like terms: 3.46t + -3.46t = 0.00 -2.5 + -3.46t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -2.5 + -3.46t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -2.5 + -3.46t + 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 + -0.706122449t + t2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + -0.706122449t + 0.5102040816 + t2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + -0.706122449t + t2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + -0.706122449t + t2 = 0 + 0.5102040816 -0.706122449t + t2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 -0.706122449t + t2 = 0.5102040816 The t term is -0.706122449t. Take half its coefficient (-0.3530612245). Square it (0.1246522282) and add it to both sides. Add '0.1246522282' to each side of the equation. -0.706122449t + 0.1246522282 + t2 = 0.5102040816 + 0.1246522282 Reorder the terms: 0.1246522282 + -0.706122449t + t2 = 0.5102040816 + 0.1246522282 Combine like terms: 0.5102040816 + 0.1246522282 = 0.6348563098 0.1246522282 + -0.706122449t + t2 = 0.6348563098 Factor a perfect square on the left side: (t + -0.3530612245)(t + -0.3530612245) = 0.6348563098 Calculate the square root of the right side: 0.796778708 Break this problem into two subproblems by setting (t + -0.3530612245) equal to 0.796778708 and -0.796778708.Subproblem 1
t + -0.3530612245 = 0.796778708 Simplifying t + -0.3530612245 = 0.796778708 Reorder the terms: -0.3530612245 + t = 0.796778708 Solving -0.3530612245 + t = 0.796778708 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3530612245' to each side of the equation. -0.3530612245 + 0.3530612245 + t = 0.796778708 + 0.3530612245 Combine like terms: -0.3530612245 + 0.3530612245 = 0.0000000000 0.0000000000 + t = 0.796778708 + 0.3530612245 t = 0.796778708 + 0.3530612245 Combine like terms: 0.796778708 + 0.3530612245 = 1.1498399325 t = 1.1498399325 Simplifying t = 1.1498399325Subproblem 2
t + -0.3530612245 = -0.796778708 Simplifying t + -0.3530612245 = -0.796778708 Reorder the terms: -0.3530612245 + t = -0.796778708 Solving -0.3530612245 + t = -0.796778708 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3530612245' to each side of the equation. -0.3530612245 + 0.3530612245 + t = -0.796778708 + 0.3530612245 Combine like terms: -0.3530612245 + 0.3530612245 = 0.0000000000 0.0000000000 + t = -0.796778708 + 0.3530612245 t = -0.796778708 + 0.3530612245 Combine like terms: -0.796778708 + 0.3530612245 = -0.4437174835 t = -0.4437174835 Simplifying t = -0.4437174835Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1498399325, -0.4437174835}
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