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Simplifying 0 = 45 + 25t + -16t2 Solving 0 = 45 + 25t + -16t2 Solving for variable 't'. Combine like terms: 0 + -45 = -45 -45 + -25t + 16t2 = 45 + 25t + -16t2 + -45 + -25t + 16t2 Reorder the terms: -45 + -25t + 16t2 = 45 + -45 + 25t + -25t + -16t2 + 16t2 Combine like terms: 45 + -45 = 0 -45 + -25t + 16t2 = 0 + 25t + -25t + -16t2 + 16t2 -45 + -25t + 16t2 = 25t + -25t + -16t2 + 16t2 Combine like terms: 25t + -25t = 0 -45 + -25t + 16t2 = 0 + -16t2 + 16t2 -45 + -25t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -45 + -25t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.8125 + -1.5625t + t2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + -1.5625t + 2.8125 + t2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + -1.5625t + t2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + -1.5625t + t2 = 0 + 2.8125 -1.5625t + t2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 -1.5625t + t2 = 2.8125 The t term is -1.5625t. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625t + 0.6103515625 + t2 = 2.8125 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625t + t2 = 2.8125 + 0.6103515625 Combine like terms: 2.8125 + 0.6103515625 = 3.4228515625 0.6103515625 + -1.5625t + t2 = 3.4228515625 Factor a perfect square on the left side: (t + -0.78125)(t + -0.78125) = 3.4228515625 Calculate the square root of the right side: 1.850095014 Break this problem into two subproblems by setting (t + -0.78125) equal to 1.850095014 and -1.850095014.Subproblem 1
t + -0.78125 = 1.850095014 Simplifying t + -0.78125 = 1.850095014 Reorder the terms: -0.78125 + t = 1.850095014 Solving -0.78125 + t = 1.850095014 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = 1.850095014 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = 1.850095014 + 0.78125 t = 1.850095014 + 0.78125 Combine like terms: 1.850095014 + 0.78125 = 2.631345014 t = 2.631345014 Simplifying t = 2.631345014Subproblem 2
t + -0.78125 = -1.850095014 Simplifying t + -0.78125 = -1.850095014 Reorder the terms: -0.78125 + t = -1.850095014 Solving -0.78125 + t = -1.850095014 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + t = -1.850095014 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + t = -1.850095014 + 0.78125 t = -1.850095014 + 0.78125 Combine like terms: -1.850095014 + 0.78125 = -1.068845014 t = -1.068845014 Simplifying t = -1.068845014Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.631345014, -1.068845014}
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