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Simplifying 10 = -16t2 + 75t + 50 Reorder the terms: 10 = 50 + 75t + -16t2 Solving 10 = 50 + 75t + -16t2 Solving for variable 't'. Combine like terms: 10 + -50 = -40 -40 + -75t + 16t2 = 50 + 75t + -16t2 + -50 + -75t + 16t2 Reorder the terms: -40 + -75t + 16t2 = 50 + -50 + 75t + -75t + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -40 + -75t + 16t2 = 0 + 75t + -75t + -16t2 + 16t2 -40 + -75t + 16t2 = 75t + -75t + -16t2 + 16t2 Combine like terms: 75t + -75t = 0 -40 + -75t + 16t2 = 0 + -16t2 + 16t2 -40 + -75t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40 + -75t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.5 + -4.6875t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -4.6875t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -4.6875t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -4.6875t + t2 = 0 + 2.5 -4.6875t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -4.6875t + t2 = 2.5 The t term is -4.6875t. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875t + 5.493164063 + t2 = 2.5 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875t + t2 = 2.5 + 5.493164063 Combine like terms: 2.5 + 5.493164063 = 7.993164063 5.493164063 + -4.6875t + t2 = 7.993164063 Factor a perfect square on the left side: (t + -2.34375)(t + -2.34375) = 7.993164063 Calculate the square root of the right side: 2.827218432 Break this problem into two subproblems by setting (t + -2.34375) equal to 2.827218432 and -2.827218432.Subproblem 1
t + -2.34375 = 2.827218432 Simplifying t + -2.34375 = 2.827218432 Reorder the terms: -2.34375 + t = 2.827218432 Solving -2.34375 + t = 2.827218432 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = 2.827218432 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = 2.827218432 + 2.34375 t = 2.827218432 + 2.34375 Combine like terms: 2.827218432 + 2.34375 = 5.170968432 t = 5.170968432 Simplifying t = 5.170968432Subproblem 2
t + -2.34375 = -2.827218432 Simplifying t + -2.34375 = -2.827218432 Reorder the terms: -2.34375 + t = -2.827218432 Solving -2.34375 + t = -2.827218432 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = -2.827218432 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = -2.827218432 + 2.34375 t = -2.827218432 + 2.34375 Combine like terms: -2.827218432 + 2.34375 = -0.483468432 t = -0.483468432 Simplifying t = -0.483468432Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.170968432, -0.483468432}
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