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Simplifying 6 + 0.577(16.38t + -15) = 11.47t + -5t2 Reorder the terms: 6 + 0.577(-15 + 16.38t) = 11.47t + -5t2 6 + (-15 * 0.577 + 16.38t * 0.577) = 11.47t + -5t2 6 + (-8.655 + 9.45126t) = 11.47t + -5t2 Combine like terms: 6 + -8.655 = -2.655 -2.655 + 9.45126t = 11.47t + -5t2 Solving -2.655 + 9.45126t = 11.47t + -5t2 Solving for variable 't'. Combine like terms: 9.45126t + -11.47t = -2.01874t -2.655 + -2.01874t + 5t2 = 11.47t + -5t2 + -11.47t + 5t2 Reorder the terms: -2.655 + -2.01874t + 5t2 = 11.47t + -11.47t + -5t2 + 5t2 Combine like terms: 11.47t + -11.47t = 0.00 -2.655 + -2.01874t + 5t2 = 0.00 + -5t2 + 5t2 -2.655 + -2.01874t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -2.655 + -2.01874t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.531 + -0.403748t + t2 = 0 Move the constant term to the right: Add '0.531' to each side of the equation. -0.531 + -0.403748t + 0.531 + t2 = 0 + 0.531 Reorder the terms: -0.531 + 0.531 + -0.403748t + t2 = 0 + 0.531 Combine like terms: -0.531 + 0.531 = 0.000 0.000 + -0.403748t + t2 = 0 + 0.531 -0.403748t + t2 = 0 + 0.531 Combine like terms: 0 + 0.531 = 0.531 -0.403748t + t2 = 0.531 The t term is -0.403748t. Take half its coefficient (-0.201874). Square it (0.04075311188) and add it to both sides. Add '0.04075311188' to each side of the equation. -0.403748t + 0.04075311188 + t2 = 0.531 + 0.04075311188 Reorder the terms: 0.04075311188 + -0.403748t + t2 = 0.531 + 0.04075311188 Combine like terms: 0.531 + 0.04075311188 = 0.57175311188 0.04075311188 + -0.403748t + t2 = 0.57175311188 Factor a perfect square on the left side: (t + -0.201874)(t + -0.201874) = 0.57175311188 Calculate the square root of the right side: 0.756143579 Break this problem into two subproblems by setting (t + -0.201874) equal to 0.756143579 and -0.756143579.Subproblem 1
t + -0.201874 = 0.756143579 Simplifying t + -0.201874 = 0.756143579 Reorder the terms: -0.201874 + t = 0.756143579 Solving -0.201874 + t = 0.756143579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.201874' to each side of the equation. -0.201874 + 0.201874 + t = 0.756143579 + 0.201874 Combine like terms: -0.201874 + 0.201874 = 0.000000 0.000000 + t = 0.756143579 + 0.201874 t = 0.756143579 + 0.201874 Combine like terms: 0.756143579 + 0.201874 = 0.958017579 t = 0.958017579 Simplifying t = 0.958017579Subproblem 2
t + -0.201874 = -0.756143579 Simplifying t + -0.201874 = -0.756143579 Reorder the terms: -0.201874 + t = -0.756143579 Solving -0.201874 + t = -0.756143579 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.201874' to each side of the equation. -0.201874 + 0.201874 + t = -0.756143579 + 0.201874 Combine like terms: -0.201874 + 0.201874 = 0.000000 0.000000 + t = -0.756143579 + 0.201874 t = -0.756143579 + 0.201874 Combine like terms: -0.756143579 + 0.201874 = -0.554269579 t = -0.554269579 Simplifying t = -0.554269579Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.958017579, -0.554269579}
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