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Simplifying 16t2 + 63t + -4 = 50 Reorder the terms: -4 + 63t + 16t2 = 50 Solving -4 + 63t + 16t2 = 50 Solving for variable 't'. Reorder the terms: -4 + -50 + 63t + 16t2 = 50 + -50 Combine like terms: -4 + -50 = -54 -54 + 63t + 16t2 = 50 + -50 Combine like terms: 50 + -50 = 0 -54 + 63t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.375 + 3.9375t + t2 = 0 Move the constant term to the right: Add '3.375' to each side of the equation. -3.375 + 3.9375t + 3.375 + t2 = 0 + 3.375 Reorder the terms: -3.375 + 3.375 + 3.9375t + t2 = 0 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + 3.9375t + t2 = 0 + 3.375 3.9375t + t2 = 0 + 3.375 Combine like terms: 0 + 3.375 = 3.375 3.9375t + t2 = 3.375 The t term is 3.9375t. Take half its coefficient (1.96875). Square it (3.875976563) and add it to both sides. Add '3.875976563' to each side of the equation. 3.9375t + 3.875976563 + t2 = 3.375 + 3.875976563 Reorder the terms: 3.875976563 + 3.9375t + t2 = 3.375 + 3.875976563 Combine like terms: 3.375 + 3.875976563 = 7.250976563 3.875976563 + 3.9375t + t2 = 7.250976563 Factor a perfect square on the left side: (t + 1.96875)(t + 1.96875) = 7.250976563 Calculate the square root of the right side: 2.692763741 Break this problem into two subproblems by setting (t + 1.96875) equal to 2.692763741 and -2.692763741.Subproblem 1
t + 1.96875 = 2.692763741 Simplifying t + 1.96875 = 2.692763741 Reorder the terms: 1.96875 + t = 2.692763741 Solving 1.96875 + t = 2.692763741 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.96875' to each side of the equation. 1.96875 + -1.96875 + t = 2.692763741 + -1.96875 Combine like terms: 1.96875 + -1.96875 = 0.00000 0.00000 + t = 2.692763741 + -1.96875 t = 2.692763741 + -1.96875 Combine like terms: 2.692763741 + -1.96875 = 0.724013741 t = 0.724013741 Simplifying t = 0.724013741Subproblem 2
t + 1.96875 = -2.692763741 Simplifying t + 1.96875 = -2.692763741 Reorder the terms: 1.96875 + t = -2.692763741 Solving 1.96875 + t = -2.692763741 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.96875' to each side of the equation. 1.96875 + -1.96875 + t = -2.692763741 + -1.96875 Combine like terms: 1.96875 + -1.96875 = 0.00000 0.00000 + t = -2.692763741 + -1.96875 t = -2.692763741 + -1.96875 Combine like terms: -2.692763741 + -1.96875 = -4.661513741 t = -4.661513741 Simplifying t = -4.661513741Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.724013741, -4.661513741}
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