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Simplifying 0 = -16t2 + 122t + 99 Reorder the terms: 0 = 99 + 122t + -16t2 Solving 0 = 99 + 122t + -16t2 Solving for variable 't'. Combine like terms: 0 + -99 = -99 -99 + -122t + 16t2 = 99 + 122t + -16t2 + -99 + -122t + 16t2 Reorder the terms: -99 + -122t + 16t2 = 99 + -99 + 122t + -122t + -16t2 + 16t2 Combine like terms: 99 + -99 = 0 -99 + -122t + 16t2 = 0 + 122t + -122t + -16t2 + 16t2 -99 + -122t + 16t2 = 122t + -122t + -16t2 + 16t2 Combine like terms: 122t + -122t = 0 -99 + -122t + 16t2 = 0 + -16t2 + 16t2 -99 + -122t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -99 + -122t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.1875 + -7.625t + t2 = 0 Move the constant term to the right: Add '6.1875' to each side of the equation. -6.1875 + -7.625t + 6.1875 + t2 = 0 + 6.1875 Reorder the terms: -6.1875 + 6.1875 + -7.625t + t2 = 0 + 6.1875 Combine like terms: -6.1875 + 6.1875 = 0.0000 0.0000 + -7.625t + t2 = 0 + 6.1875 -7.625t + t2 = 0 + 6.1875 Combine like terms: 0 + 6.1875 = 6.1875 -7.625t + t2 = 6.1875 The t term is -7.625t. Take half its coefficient (-3.8125). Square it (14.53515625) and add it to both sides. Add '14.53515625' to each side of the equation. -7.625t + 14.53515625 + t2 = 6.1875 + 14.53515625 Reorder the terms: 14.53515625 + -7.625t + t2 = 6.1875 + 14.53515625 Combine like terms: 6.1875 + 14.53515625 = 20.72265625 14.53515625 + -7.625t + t2 = 20.72265625 Factor a perfect square on the left side: (t + -3.8125)(t + -3.8125) = 20.72265625 Calculate the square root of the right side: 4.552214434 Break this problem into two subproblems by setting (t + -3.8125) equal to 4.552214434 and -4.552214434.Subproblem 1
t + -3.8125 = 4.552214434 Simplifying t + -3.8125 = 4.552214434 Reorder the terms: -3.8125 + t = 4.552214434 Solving -3.8125 + t = 4.552214434 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = 4.552214434 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = 4.552214434 + 3.8125 t = 4.552214434 + 3.8125 Combine like terms: 4.552214434 + 3.8125 = 8.364714434 t = 8.364714434 Simplifying t = 8.364714434Subproblem 2
t + -3.8125 = -4.552214434 Simplifying t + -3.8125 = -4.552214434 Reorder the terms: -3.8125 + t = -4.552214434 Solving -3.8125 + t = -4.552214434 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = -4.552214434 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = -4.552214434 + 3.8125 t = -4.552214434 + 3.8125 Combine like terms: -4.552214434 + 3.8125 = -0.739714434 t = -0.739714434 Simplifying t = -0.739714434Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.364714434, -0.739714434}
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