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Simplifying 1.8 = 5t + -1.6t2 Solving 1.8 = 5t + -1.6t2 Solving for variable 't'. Reorder the terms: 1.8 + -5t + 1.6t2 = 5t + -5t + -1.6t2 + 1.6t2 Combine like terms: 5t + -5t = 0 1.8 + -5t + 1.6t2 = 0 + -1.6t2 + 1.6t2 1.8 + -5t + 1.6t2 = -1.6t2 + 1.6t2 Combine like terms: -1.6t2 + 1.6t2 = 0.0 1.8 + -5t + 1.6t2 = 0.0 Begin completing the square. Divide all terms by 1.6 the coefficient of the squared term: Divide each side by '1.6'. 1.125 + -3.125t + t2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -3.125t + -1.125 + t2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -3.125t + t2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -3.125t + t2 = 0 + -1.125 -3.125t + t2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -3.125t + t2 = -1.125 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 = -1.125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = -1.125 + 2.44140625 Combine like terms: -1.125 + 2.44140625 = 1.31640625 2.44140625 + -3.125t + t2 = 1.31640625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (t + -1.5625) equal to 1.147347484 and -1.147347484.Subproblem 1
t + -1.5625 = 1.147347484 Simplifying t + -1.5625 = 1.147347484 Reorder the terms: -1.5625 + t = 1.147347484 Solving -1.5625 + t = 1.147347484 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 = 1.147347484 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 1.147347484 + 1.5625 t = 1.147347484 + 1.5625 Combine like terms: 1.147347484 + 1.5625 = 2.709847484 t = 2.709847484 Simplifying t = 2.709847484Subproblem 2
t + -1.5625 = -1.147347484 Simplifying t + -1.5625 = -1.147347484 Reorder the terms: -1.5625 + t = -1.147347484 Solving -1.5625 + t = -1.147347484 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 = -1.147347484 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -1.147347484 + 1.5625 t = -1.147347484 + 1.5625 Combine like terms: -1.147347484 + 1.5625 = 0.415152516 t = 0.415152516 Simplifying t = 0.415152516Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.709847484, 0.415152516}
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