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Simplifying 17 = 55t + -5t2 Solving 17 = 55t + -5t2 Solving for variable 't'. Reorder the terms: 17 + -55t + 5t2 = 55t + -55t + -5t2 + 5t2 Combine like terms: 55t + -55t = 0 17 + -55t + 5t2 = 0 + -5t2 + 5t2 17 + -55t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 17 + -55t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.4 + -11t + t2 = 0 Move the constant term to the right: Add '-3.4' to each side of the equation. 3.4 + -11t + -3.4 + t2 = 0 + -3.4 Reorder the terms: 3.4 + -3.4 + -11t + t2 = 0 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + -11t + t2 = 0 + -3.4 -11t + t2 = 0 + -3.4 Combine like terms: 0 + -3.4 = -3.4 -11t + t2 = -3.4 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = -3.4 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -3.4 + 30.25 Combine like terms: -3.4 + 30.25 = 26.85 30.25 + -11t + t2 = 26.85 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 26.85 Calculate the square root of the right side: 5.181698563 Break this problem into two subproblems by setting (t + -5.5) equal to 5.181698563 and -5.181698563.Subproblem 1
t + -5.5 = 5.181698563 Simplifying t + -5.5 = 5.181698563 Reorder the terms: -5.5 + t = 5.181698563 Solving -5.5 + t = 5.181698563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 5.181698563 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 5.181698563 + 5.5 t = 5.181698563 + 5.5 Combine like terms: 5.181698563 + 5.5 = 10.681698563 t = 10.681698563 Simplifying t = 10.681698563Subproblem 2
t + -5.5 = -5.181698563 Simplifying t + -5.5 = -5.181698563 Reorder the terms: -5.5 + t = -5.181698563 Solving -5.5 + t = -5.181698563 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -5.181698563 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -5.181698563 + 5.5 t = -5.181698563 + 5.5 Combine like terms: -5.181698563 + 5.5 = 0.318301437 t = 0.318301437 Simplifying t = 0.318301437Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.681698563, 0.318301437}
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