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Simplifying -16t2 + 48t + 864 = t Reorder the terms: 864 + 48t + -16t2 = t Solving 864 + 48t + -16t2 = t Solving for variable 't'. Reorder the terms: 864 + 48t + -1t + -16t2 = t + -1t Combine like terms: 48t + -1t = 47t 864 + 47t + -16t2 = t + -1t Combine like terms: t + -1t = 0 864 + 47t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -54 + -2.9375t + t2 = 0 Move the constant term to the right: Add '54' to each side of the equation. -54 + -2.9375t + 54 + t2 = 0 + 54 Reorder the terms: -54 + 54 + -2.9375t + t2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -2.9375t + t2 = 0 + 54 -2.9375t + t2 = 0 + 54 Combine like terms: 0 + 54 = 54 -2.9375t + t2 = 54 The t term is -2.9375t. Take half its coefficient (-1.46875). Square it (2.157226563) and add it to both sides. Add '2.157226563' to each side of the equation. -2.9375t + 2.157226563 + t2 = 54 + 2.157226563 Reorder the terms: 2.157226563 + -2.9375t + t2 = 54 + 2.157226563 Combine like terms: 54 + 2.157226563 = 56.157226563 2.157226563 + -2.9375t + t2 = 56.157226563 Factor a perfect square on the left side: (t + -1.46875)(t + -1.46875) = 56.157226563 Calculate the square root of the right side: 7.493812552 Break this problem into two subproblems by setting (t + -1.46875) equal to 7.493812552 and -7.493812552.Subproblem 1
t + -1.46875 = 7.493812552 Simplifying t + -1.46875 = 7.493812552 Reorder the terms: -1.46875 + t = 7.493812552 Solving -1.46875 + t = 7.493812552 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.46875' to each side of the equation. -1.46875 + 1.46875 + t = 7.493812552 + 1.46875 Combine like terms: -1.46875 + 1.46875 = 0.00000 0.00000 + t = 7.493812552 + 1.46875 t = 7.493812552 + 1.46875 Combine like terms: 7.493812552 + 1.46875 = 8.962562552 t = 8.962562552 Simplifying t = 8.962562552Subproblem 2
t + -1.46875 = -7.493812552 Simplifying t + -1.46875 = -7.493812552 Reorder the terms: -1.46875 + t = -7.493812552 Solving -1.46875 + t = -7.493812552 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.46875' to each side of the equation. -1.46875 + 1.46875 + t = -7.493812552 + 1.46875 Combine like terms: -1.46875 + 1.46875 = 0.00000 0.00000 + t = -7.493812552 + 1.46875 t = -7.493812552 + 1.46875 Combine like terms: -7.493812552 + 1.46875 = -6.025062552 t = -6.025062552 Simplifying t = -6.025062552Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.962562552, -6.025062552}
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