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Simplifying 0.0795t2 + -0.91t + 1.789 = 0 Reorder the terms: 1.789 + -0.91t + 0.0795t2 = 0 Solving 1.789 + -0.91t + 0.0795t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0795 the coefficient of the squared term: Divide each side by '0.0795'. 22.50314465 + -11.44654088t + t2 = 0 Move the constant term to the right: Add '-22.50314465' to each side of the equation. 22.50314465 + -11.44654088t + -22.50314465 + t2 = 0 + -22.50314465 Reorder the terms: 22.50314465 + -22.50314465 + -11.44654088t + t2 = 0 + -22.50314465 Combine like terms: 22.50314465 + -22.50314465 = 0.00000000 0.00000000 + -11.44654088t + t2 = 0 + -22.50314465 -11.44654088t + t2 = 0 + -22.50314465 Combine like terms: 0 + -22.50314465 = -22.50314465 -11.44654088t + t2 = -22.50314465 The t term is -11.44654088t. Take half its coefficient (-5.72327044). Square it (32.75582453) and add it to both sides. Add '32.75582453' to each side of the equation. -11.44654088t + 32.75582453 + t2 = -22.50314465 + 32.75582453 Reorder the terms: 32.75582453 + -11.44654088t + t2 = -22.50314465 + 32.75582453 Combine like terms: -22.50314465 + 32.75582453 = 10.25267988 32.75582453 + -11.44654088t + t2 = 10.25267988 Factor a perfect square on the left side: (t + -5.72327044)(t + -5.72327044) = 10.25267988 Calculate the square root of the right side: 3.201980618 Break this problem into two subproblems by setting (t + -5.72327044) equal to 3.201980618 and -3.201980618.Subproblem 1
t + -5.72327044 = 3.201980618 Simplifying t + -5.72327044 = 3.201980618 Reorder the terms: -5.72327044 + t = 3.201980618 Solving -5.72327044 + t = 3.201980618 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.72327044' to each side of the equation. -5.72327044 + 5.72327044 + t = 3.201980618 + 5.72327044 Combine like terms: -5.72327044 + 5.72327044 = 0.00000000 0.00000000 + t = 3.201980618 + 5.72327044 t = 3.201980618 + 5.72327044 Combine like terms: 3.201980618 + 5.72327044 = 8.925251058 t = 8.925251058 Simplifying t = 8.925251058Subproblem 2
t + -5.72327044 = -3.201980618 Simplifying t + -5.72327044 = -3.201980618 Reorder the terms: -5.72327044 + t = -3.201980618 Solving -5.72327044 + t = -3.201980618 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.72327044' to each side of the equation. -5.72327044 + 5.72327044 + t = -3.201980618 + 5.72327044 Combine like terms: -5.72327044 + 5.72327044 = 0.00000000 0.00000000 + t = -3.201980618 + 5.72327044 t = -3.201980618 + 5.72327044 Combine like terms: -3.201980618 + 5.72327044 = 2.521289822 t = 2.521289822 Simplifying t = 2.521289822Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.925251058, 2.521289822}
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