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Simplifying 0 = 3 + 10t + -5t2 Solving 0 = 3 + 10t + -5t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -10t + 5t2 = 3 + 10t + -5t2 + -3 + -10t + 5t2 Reorder the terms: -3 + -10t + 5t2 = 3 + -3 + 10t + -10t + -5t2 + 5t2 Combine like terms: 3 + -3 = 0 -3 + -10t + 5t2 = 0 + 10t + -10t + -5t2 + 5t2 -3 + -10t + 5t2 = 10t + -10t + -5t2 + 5t2 Combine like terms: 10t + -10t = 0 -3 + -10t + 5t2 = 0 + -5t2 + 5t2 -3 + -10t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -3 + -10t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + -2t + t2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -2t + 0.6 + t2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -2t + t2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -2t + t2 = 0 + 0.6 -2t + t2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -2t + t2 = 0.6 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 0.6 + 1 Reorder the terms: 1 + -2t + t2 = 0.6 + 1 Combine like terms: 0.6 + 1 = 1.6 1 + -2t + t2 = 1.6 Factor a perfect square on the left side: (t + -1)(t + -1) = 1.6 Calculate the square root of the right side: 1.264911064 Break this problem into two subproblems by setting (t + -1) equal to 1.264911064 and -1.264911064.Subproblem 1
t + -1 = 1.264911064 Simplifying t + -1 = 1.264911064 Reorder the terms: -1 + t = 1.264911064 Solving -1 + t = 1.264911064 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 1.264911064 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.264911064 + 1 t = 1.264911064 + 1 Combine like terms: 1.264911064 + 1 = 2.264911064 t = 2.264911064 Simplifying t = 2.264911064Subproblem 2
t + -1 = -1.264911064 Simplifying t + -1 = -1.264911064 Reorder the terms: -1 + t = -1.264911064 Solving -1 + t = -1.264911064 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -1.264911064 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.264911064 + 1 t = -1.264911064 + 1 Combine like terms: -1.264911064 + 1 = -0.264911064 t = -0.264911064 Simplifying t = -0.264911064Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.264911064, -0.264911064}
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