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Simplifying 93 = 201t + 16t2 Solving 93 = 201t + 16t2 Solving for variable 't'. Reorder the terms: 93 + -201t + -16t2 = 201t + -201t + 16t2 + -16t2 Combine like terms: 201t + -201t = 0 93 + -201t + -16t2 = 0 + 16t2 + -16t2 93 + -201t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 93 + -201t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5.8125 + 12.5625t + t2 = 0 Move the constant term to the right: Add '5.8125' to each side of the equation. -5.8125 + 12.5625t + 5.8125 + t2 = 0 + 5.8125 Reorder the terms: -5.8125 + 5.8125 + 12.5625t + t2 = 0 + 5.8125 Combine like terms: -5.8125 + 5.8125 = 0.0000 0.0000 + 12.5625t + t2 = 0 + 5.8125 12.5625t + t2 = 0 + 5.8125 Combine like terms: 0 + 5.8125 = 5.8125 12.5625t + t2 = 5.8125 The t term is 12.5625t. Take half its coefficient (6.28125). Square it (39.45410156) and add it to both sides. Add '39.45410156' to each side of the equation. 12.5625t + 39.45410156 + t2 = 5.8125 + 39.45410156 Reorder the terms: 39.45410156 + 12.5625t + t2 = 5.8125 + 39.45410156 Combine like terms: 5.8125 + 39.45410156 = 45.26660156 39.45410156 + 12.5625t + t2 = 45.26660156 Factor a perfect square on the left side: (t + 6.28125)(t + 6.28125) = 45.26660156 Calculate the square root of the right side: 6.728045895 Break this problem into two subproblems by setting (t + 6.28125) equal to 6.728045895 and -6.728045895.Subproblem 1
t + 6.28125 = 6.728045895 Simplifying t + 6.28125 = 6.728045895 Reorder the terms: 6.28125 + t = 6.728045895 Solving 6.28125 + t = 6.728045895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.28125' to each side of the equation. 6.28125 + -6.28125 + t = 6.728045895 + -6.28125 Combine like terms: 6.28125 + -6.28125 = 0.00000 0.00000 + t = 6.728045895 + -6.28125 t = 6.728045895 + -6.28125 Combine like terms: 6.728045895 + -6.28125 = 0.446795895 t = 0.446795895 Simplifying t = 0.446795895Subproblem 2
t + 6.28125 = -6.728045895 Simplifying t + 6.28125 = -6.728045895 Reorder the terms: 6.28125 + t = -6.728045895 Solving 6.28125 + t = -6.728045895 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.28125' to each side of the equation. 6.28125 + -6.28125 + t = -6.728045895 + -6.28125 Combine like terms: 6.28125 + -6.28125 = 0.00000 0.00000 + t = -6.728045895 + -6.28125 t = -6.728045895 + -6.28125 Combine like terms: -6.728045895 + -6.28125 = -13.009295895 t = -13.009295895 Simplifying t = -13.009295895Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.446795895, -13.009295895}
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