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Simplifying 0 = -16t2 + 160t + 3 Reorder the terms: 0 = 3 + 160t + -16t2 Solving 0 = 3 + 160t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -160t + 16t2 = 3 + 160t + -16t2 + -3 + -160t + 16t2 Reorder the terms: -3 + -160t + 16t2 = 3 + -3 + 160t + -160t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2 -3 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 -3 + -160t + 16t2 = 0 + -16t2 + 16t2 -3 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -160t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -10t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -10t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -10t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -10t + t2 = 0 + 0.1875 -10t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -10t + t2 = 0.1875 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 0.1875 + 25 Reorder the terms: 25 + -10t + t2 = 0.1875 + 25 Combine like terms: 0.1875 + 25 = 25.1875 25 + -10t + t2 = 25.1875 Factor a perfect square on the left side: (t + -5)(t + -5) = 25.1875 Calculate the square root of the right side: 5.018714975 Break this problem into two subproblems by setting (t + -5) equal to 5.018714975 and -5.018714975.Subproblem 1
t + -5 = 5.018714975 Simplifying t + -5 = 5.018714975 Reorder the terms: -5 + t = 5.018714975 Solving -5 + t = 5.018714975 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.018714975 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.018714975 + 5 t = 5.018714975 + 5 Combine like terms: 5.018714975 + 5 = 10.018714975 t = 10.018714975 Simplifying t = 10.018714975Subproblem 2
t + -5 = -5.018714975 Simplifying t + -5 = -5.018714975 Reorder the terms: -5 + t = -5.018714975 Solving -5 + t = -5.018714975 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.018714975 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.018714975 + 5 t = -5.018714975 + 5 Combine like terms: -5.018714975 + 5 = -0.018714975 t = -0.018714975 Simplifying t = -0.018714975Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.018714975, -0.018714975}
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