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Simplifying t2 = 3.125t + -1.5 Reorder the terms: t2 = -1.5 + 3.125t Solving t2 = -1.5 + 3.125t Solving for variable 't'. Reorder the terms: 1.5 + -3.125t + t2 = -1.5 + 3.125t + 1.5 + -3.125t Reorder the terms: 1.5 + -3.125t + t2 = -1.5 + 1.5 + 3.125t + -3.125t Combine like terms: -1.5 + 1.5 = 0.0 1.5 + -3.125t + t2 = 0.0 + 3.125t + -3.125t 1.5 + -3.125t + t2 = 3.125t + -3.125t Combine like terms: 3.125t + -3.125t = 0.000 1.5 + -3.125t + t2 = 0.000 Begin completing the square. Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.125t + -1.5 + t2 = 0.000 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.125t + t2 = 0.000 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.125t + t2 = 0.000 + -1.5 -3.125t + t2 = 0.000 + -1.5 Combine like terms: 0.000 + -1.5 = -1.5 -3.125t + t2 = -1.5 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = -1.5 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = -1.5 + 2.44140625 Combine like terms: -1.5 + 2.44140625 = 0.94140625 2.44140625 + -3.125t + t2 = 0.94140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (t + -1.5625) equal to 0.970260919 and -0.970260919.Subproblem 1
t + -1.5625 = 0.970260919 Simplifying t + -1.5625 = 0.970260919 Reorder the terms: -1.5625 + t = 0.970260919 Solving -1.5625 + t = 0.970260919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 0.970260919 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 0.970260919 + 1.5625 t = 0.970260919 + 1.5625 Combine like terms: 0.970260919 + 1.5625 = 2.532760919 t = 2.532760919 Simplifying t = 2.532760919Subproblem 2
t + -1.5625 = -0.970260919 Simplifying t + -1.5625 = -0.970260919 Reorder the terms: -1.5625 + t = -0.970260919 Solving -1.5625 + t = -0.970260919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -0.970260919 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -0.970260919 + 1.5625 t = -0.970260919 + 1.5625 Combine like terms: -0.970260919 + 1.5625 = 0.592239081 t = 0.592239081 Simplifying t = 0.592239081Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.532760919, 0.592239081}
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