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Simplifying 23 = -16t2 + 227t + 0 Reorder the terms: 23 = 0 + 227t + -16t2 Remove the zero: 23 = 227t + -16t2 Solving 23 = 227t + -16t2 Solving for variable 't'. Reorder the terms: 23 + -227t + 16t2 = 227t + -227t + -16t2 + 16t2 Combine like terms: 227t + -227t = 0 23 + -227t + 16t2 = 0 + -16t2 + 16t2 23 + -227t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 23 + -227t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.4375 + -14.1875t + t2 = 0 Move the constant term to the right: Add '-1.4375' to each side of the equation. 1.4375 + -14.1875t + -1.4375 + t2 = 0 + -1.4375 Reorder the terms: 1.4375 + -1.4375 + -14.1875t + t2 = 0 + -1.4375 Combine like terms: 1.4375 + -1.4375 = 0.0000 0.0000 + -14.1875t + t2 = 0 + -1.4375 -14.1875t + t2 = 0 + -1.4375 Combine like terms: 0 + -1.4375 = -1.4375 -14.1875t + t2 = -1.4375 The t term is -14.1875t. Take half its coefficient (-7.09375). Square it (50.32128906) and add it to both sides. Add '50.32128906' to each side of the equation. -14.1875t + 50.32128906 + t2 = -1.4375 + 50.32128906 Reorder the terms: 50.32128906 + -14.1875t + t2 = -1.4375 + 50.32128906 Combine like terms: -1.4375 + 50.32128906 = 48.88378906 50.32128906 + -14.1875t + t2 = 48.88378906 Factor a perfect square on the left side: (t + -7.09375)(t + -7.09375) = 48.88378906 Calculate the square root of the right side: 6.991694291 Break this problem into two subproblems by setting (t + -7.09375) equal to 6.991694291 and -6.991694291.Subproblem 1
t + -7.09375 = 6.991694291 Simplifying t + -7.09375 = 6.991694291 Reorder the terms: -7.09375 + t = 6.991694291 Solving -7.09375 + t = 6.991694291 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.09375' to each side of the equation. -7.09375 + 7.09375 + t = 6.991694291 + 7.09375 Combine like terms: -7.09375 + 7.09375 = 0.00000 0.00000 + t = 6.991694291 + 7.09375 t = 6.991694291 + 7.09375 Combine like terms: 6.991694291 + 7.09375 = 14.085444291 t = 14.085444291 Simplifying t = 14.085444291Subproblem 2
t + -7.09375 = -6.991694291 Simplifying t + -7.09375 = -6.991694291 Reorder the terms: -7.09375 + t = -6.991694291 Solving -7.09375 + t = -6.991694291 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.09375' to each side of the equation. -7.09375 + 7.09375 + t = -6.991694291 + 7.09375 Combine like terms: -7.09375 + 7.09375 = 0.00000 0.00000 + t = -6.991694291 + 7.09375 t = -6.991694291 + 7.09375 Combine like terms: -6.991694291 + 7.09375 = 0.102055709 t = 0.102055709 Simplifying t = 0.102055709Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.085444291, 0.102055709}
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