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Simplifying 2 = 55t + -5t2 Solving 2 = 55t + -5t2 Solving for variable 't'. Reorder the terms: 2 + -55t + 5t2 = 55t + -55t + -5t2 + 5t2 Combine like terms: 55t + -55t = 0 2 + -55t + 5t2 = 0 + -5t2 + 5t2 2 + -55t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 2 + -55t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -11t + t2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -11t + -0.4 + t2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -11t + t2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -11t + t2 = 0 + -0.4 -11t + t2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -11t + t2 = -0.4 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 = -0.4 + 30.25 Reorder the terms: 30.25 + -11t + t2 = -0.4 + 30.25 Combine like terms: -0.4 + 30.25 = 29.85 30.25 + -11t + t2 = 29.85 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 29.85 Calculate the square root of the right side: 5.463515352 Break this problem into two subproblems by setting (t + -5.5) equal to 5.463515352 and -5.463515352.Subproblem 1
t + -5.5 = 5.463515352 Simplifying t + -5.5 = 5.463515352 Reorder the terms: -5.5 + t = 5.463515352 Solving -5.5 + t = 5.463515352 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 = 5.463515352 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 5.463515352 + 5.5 t = 5.463515352 + 5.5 Combine like terms: 5.463515352 + 5.5 = 10.963515352 t = 10.963515352 Simplifying t = 10.963515352Subproblem 2
t + -5.5 = -5.463515352 Simplifying t + -5.5 = -5.463515352 Reorder the terms: -5.5 + t = -5.463515352 Solving -5.5 + t = -5.463515352 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 = -5.463515352 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -5.463515352 + 5.5 t = -5.463515352 + 5.5 Combine like terms: -5.463515352 + 5.5 = 0.036484648 t = 0.036484648 Simplifying t = 0.036484648Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.963515352, 0.036484648}
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