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Simplifying 4 = 3 + 5t + -5t2 Solving 4 = 3 + 5t + -5t2 Solving for variable 't'. Combine like terms: 4 + -3 = 1 1 + -5t + 5t2 = 3 + 5t + -5t2 + -3 + -5t + 5t2 Reorder the terms: 1 + -5t + 5t2 = 3 + -3 + 5t + -5t + -5t2 + 5t2 Combine like terms: 3 + -3 = 0 1 + -5t + 5t2 = 0 + 5t + -5t + -5t2 + 5t2 1 + -5t + 5t2 = 5t + -5t + -5t2 + 5t2 Combine like terms: 5t + -5t = 0 1 + -5t + 5t2 = 0 + -5t2 + 5t2 1 + -5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 1 + -5t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -1t + t2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1t + -0.2 + t2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1t + t2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1t + t2 = 0 + -0.2 -1t + t2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1t + t2 = -0.2 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = -0.2 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -0.2 + 0.25 Combine like terms: -0.2 + 0.25 = 0.05 0.25 + -1t + t2 = 0.05 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (t + -0.5) equal to 0.223606798 and -0.223606798.Subproblem 1
t + -0.5 = 0.223606798 Simplifying t + -0.5 = 0.223606798 Reorder the terms: -0.5 + t = 0.223606798 Solving -0.5 + t = 0.223606798 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.223606798 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.223606798 + 0.5 t = 0.223606798 + 0.5 Combine like terms: 0.223606798 + 0.5 = 0.723606798 t = 0.723606798 Simplifying t = 0.723606798Subproblem 2
t + -0.5 = -0.223606798 Simplifying t + -0.5 = -0.223606798 Reorder the terms: -0.5 + t = -0.223606798 Solving -0.5 + t = -0.223606798 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -0.223606798 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -0.223606798 + 0.5 t = -0.223606798 + 0.5 Combine like terms: -0.223606798 + 0.5 = 0.276393202 t = 0.276393202 Simplifying t = 0.276393202Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.723606798, 0.276393202}
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