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Simplifying 0 = -5t2 + 40t + 2 Reorder the terms: 0 = 2 + 40t + -5t2 Solving 0 = 2 + 40t + -5t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -40t + 5t2 = 2 + 40t + -5t2 + -2 + -40t + 5t2 Reorder the terms: -2 + -40t + 5t2 = 2 + -2 + 40t + -40t + -5t2 + 5t2 Combine like terms: 2 + -2 = 0 -2 + -40t + 5t2 = 0 + 40t + -40t + -5t2 + 5t2 -2 + -40t + 5t2 = 40t + -40t + -5t2 + 5t2 Combine like terms: 40t + -40t = 0 -2 + -40t + 5t2 = 0 + -5t2 + 5t2 -2 + -40t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -2 + -40t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -8t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -8t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -8t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -8t + t2 = 0 + 0.4 -8t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -8t + t2 = 0.4 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 0.4 + 16 Reorder the terms: 16 + -8t + t2 = 0.4 + 16 Combine like terms: 0.4 + 16 = 16.4 16 + -8t + t2 = 16.4 Factor a perfect square on the left side: (t + -4)(t + -4) = 16.4 Calculate the square root of the right side: 4.049691346 Break this problem into two subproblems by setting (t + -4) equal to 4.049691346 and -4.049691346.Subproblem 1
t + -4 = 4.049691346 Simplifying t + -4 = 4.049691346 Reorder the terms: -4 + t = 4.049691346 Solving -4 + t = 4.049691346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.049691346 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.049691346 + 4 t = 4.049691346 + 4 Combine like terms: 4.049691346 + 4 = 8.049691346 t = 8.049691346 Simplifying t = 8.049691346Subproblem 2
t + -4 = -4.049691346 Simplifying t + -4 = -4.049691346 Reorder the terms: -4 + t = -4.049691346 Solving -4 + t = -4.049691346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.049691346 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.049691346 + 4 t = -4.049691346 + 4 Combine like terms: -4.049691346 + 4 = -0.049691346 t = -0.049691346 Simplifying t = -0.049691346Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.049691346, -0.049691346}
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