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Simplifying 300 + -9t + -9.8t2 = 0 Solving 300 + -9t + -9.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -30.6122449 + 0.9183673469t + t2 = 0 Move the constant term to the right: Add '30.6122449' to each side of the equation. -30.6122449 + 0.9183673469t + 30.6122449 + t2 = 0 + 30.6122449 Reorder the terms: -30.6122449 + 30.6122449 + 0.9183673469t + t2 = 0 + 30.6122449 Combine like terms: -30.6122449 + 30.6122449 = 0.0000000 0.0000000 + 0.9183673469t + t2 = 0 + 30.6122449 0.9183673469t + t2 = 0 + 30.6122449 Combine like terms: 0 + 30.6122449 = 30.6122449 0.9183673469t + t2 = 30.6122449 The t term is 0.9183673469t. Take half its coefficient (0.4591836735). Square it (0.2108496460) and add it to both sides. Add '0.2108496460' to each side of the equation. 0.9183673469t + 0.2108496460 + t2 = 30.6122449 + 0.2108496460 Reorder the terms: 0.2108496460 + 0.9183673469t + t2 = 30.6122449 + 0.2108496460 Combine like terms: 30.6122449 + 0.2108496460 = 30.823094546 0.2108496460 + 0.9183673469t + t2 = 30.823094546 Factor a perfect square on the left side: (t + 0.4591836735)(t + 0.4591836735) = 30.823094546 Calculate the square root of the right side: 5.551855054 Break this problem into two subproblems by setting (t + 0.4591836735) equal to 5.551855054 and -5.551855054.Subproblem 1
t + 0.4591836735 = 5.551855054 Simplifying t + 0.4591836735 = 5.551855054 Reorder the terms: 0.4591836735 + t = 5.551855054 Solving 0.4591836735 + t = 5.551855054 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4591836735' to each side of the equation. 0.4591836735 + -0.4591836735 + t = 5.551855054 + -0.4591836735 Combine like terms: 0.4591836735 + -0.4591836735 = 0.0000000000 0.0000000000 + t = 5.551855054 + -0.4591836735 t = 5.551855054 + -0.4591836735 Combine like terms: 5.551855054 + -0.4591836735 = 5.0926713805 t = 5.0926713805 Simplifying t = 5.0926713805Subproblem 2
t + 0.4591836735 = -5.551855054 Simplifying t + 0.4591836735 = -5.551855054 Reorder the terms: 0.4591836735 + t = -5.551855054 Solving 0.4591836735 + t = -5.551855054 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4591836735' to each side of the equation. 0.4591836735 + -0.4591836735 + t = -5.551855054 + -0.4591836735 Combine like terms: 0.4591836735 + -0.4591836735 = 0.0000000000 0.0000000000 + t = -5.551855054 + -0.4591836735 t = -5.551855054 + -0.4591836735 Combine like terms: -5.551855054 + -0.4591836735 = -6.0110387275 t = -6.0110387275 Simplifying t = -6.0110387275Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.0926713805, -6.0110387275}
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