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Simplifying -80.8 = -4.905t2 + 1.65t Reorder the terms: -80.8 = 1.65t + -4.905t2 Solving -80.8 = 1.65t + -4.905t2 Solving for variable 't'. Reorder the terms: -80.8 + -1.65t + 4.905t2 = 1.65t + -1.65t + -4.905t2 + 4.905t2 Combine like terms: 1.65t + -1.65t = 0.00 -80.8 + -1.65t + 4.905t2 = 0.00 + -4.905t2 + 4.905t2 -80.8 + -1.65t + 4.905t2 = -4.905t2 + 4.905t2 Combine like terms: -4.905t2 + 4.905t2 = 0.000 -80.8 + -1.65t + 4.905t2 = 0.000 Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -16.47298675 + -0.3363914373t + t2 = 0 Move the constant term to the right: Add '16.47298675' to each side of the equation. -16.47298675 + -0.3363914373t + 16.47298675 + t2 = 0 + 16.47298675 Reorder the terms: -16.47298675 + 16.47298675 + -0.3363914373t + t2 = 0 + 16.47298675 Combine like terms: -16.47298675 + 16.47298675 = 0.00000000 0.00000000 + -0.3363914373t + t2 = 0 + 16.47298675 -0.3363914373t + t2 = 0 + 16.47298675 Combine like terms: 0 + 16.47298675 = 16.47298675 -0.3363914373t + t2 = 16.47298675 The t term is -0.3363914373t. Take half its coefficient (-0.1681957187). Square it (0.02828979979) and add it to both sides. Add '0.02828979979' to each side of the equation. -0.3363914373t + 0.02828979979 + t2 = 16.47298675 + 0.02828979979 Reorder the terms: 0.02828979979 + -0.3363914373t + t2 = 16.47298675 + 0.02828979979 Combine like terms: 16.47298675 + 0.02828979979 = 16.50127654979 0.02828979979 + -0.3363914373t + t2 = 16.50127654979 Factor a perfect square on the left side: (t + -0.1681957187)(t + -0.1681957187) = 16.50127654979 Calculate the square root of the right side: 4.062176332 Break this problem into two subproblems by setting (t + -0.1681957187) equal to 4.062176332 and -4.062176332.Subproblem 1
t + -0.1681957187 = 4.062176332 Simplifying t + -0.1681957187 = 4.062176332 Reorder the terms: -0.1681957187 + t = 4.062176332 Solving -0.1681957187 + t = 4.062176332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1681957187' to each side of the equation. -0.1681957187 + 0.1681957187 + t = 4.062176332 + 0.1681957187 Combine like terms: -0.1681957187 + 0.1681957187 = 0.0000000000 0.0000000000 + t = 4.062176332 + 0.1681957187 t = 4.062176332 + 0.1681957187 Combine like terms: 4.062176332 + 0.1681957187 = 4.2303720507 t = 4.2303720507 Simplifying t = 4.2303720507Subproblem 2
t + -0.1681957187 = -4.062176332 Simplifying t + -0.1681957187 = -4.062176332 Reorder the terms: -0.1681957187 + t = -4.062176332 Solving -0.1681957187 + t = -4.062176332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1681957187' to each side of the equation. -0.1681957187 + 0.1681957187 + t = -4.062176332 + 0.1681957187 Combine like terms: -0.1681957187 + 0.1681957187 = 0.0000000000 0.0000000000 + t = -4.062176332 + 0.1681957187 t = -4.062176332 + 0.1681957187 Combine like terms: -4.062176332 + 0.1681957187 = -3.8939806133 t = -3.8939806133 Simplifying t = -3.8939806133Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.2303720507, -3.8939806133}
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