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Simplifying 32 = 55t + -5t2 Solving 32 = 55t + -5t2 Solving for variable 't'. Reorder the terms: 32 + -55t + 5t2 = 55t + -55t + -5t2 + 5t2 Combine like terms: 55t + -55t = 0 32 + -55t + 5t2 = 0 + -5t2 + 5t2 32 + -55t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 32 + -55t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.4 + -11t + t2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + -11t + -6.4 + t2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + -11t + t2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + -11t + t2 = 0 + -6.4 -11t + t2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 -11t + t2 = -6.4 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 = -6.4 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -6.4 + 30.25 Combine like terms: -6.4 + 30.25 = 23.85 30.25 + -11t + t2 = 23.85 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 23.85 Calculate the square root of the right side: 4.883646179 Break this problem into two subproblems by setting (t + -5.5) equal to 4.883646179 and -4.883646179.Subproblem 1
t + -5.5 = 4.883646179 Simplifying t + -5.5 = 4.883646179 Reorder the terms: -5.5 + t = 4.883646179 Solving -5.5 + t = 4.883646179 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 = 4.883646179 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 4.883646179 + 5.5 t = 4.883646179 + 5.5 Combine like terms: 4.883646179 + 5.5 = 10.383646179 t = 10.383646179 Simplifying t = 10.383646179Subproblem 2
t + -5.5 = -4.883646179 Simplifying t + -5.5 = -4.883646179 Reorder the terms: -5.5 + t = -4.883646179 Solving -5.5 + t = -4.883646179 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 = -4.883646179 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -4.883646179 + 5.5 t = -4.883646179 + 5.5 Combine like terms: -4.883646179 + 5.5 = 0.616353821 t = 0.616353821 Simplifying t = 0.616353821Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.383646179, 0.616353821}
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