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Simplifying 10 = 16t + -5t2 Solving 10 = 16t + -5t2 Solving for variable 't'. Reorder the terms: 10 + -16t + 5t2 = 16t + -16t + -5t2 + 5t2 Combine like terms: 16t + -16t = 0 10 + -16t + 5t2 = 0 + -5t2 + 5t2 10 + -16t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 10 + -16t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -3.2t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.2t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -3.2t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.2t + t2 = 0 + -2 -3.2t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.2t + t2 = -2 The t term is -3.2t. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2t + 2.56 + t2 = -2 + 2.56 Reorder the terms: 2.56 + -3.2t + t2 = -2 + 2.56 Combine like terms: -2 + 2.56 = 0.56 2.56 + -3.2t + t2 = 0.56 Factor a perfect square on the left side: (t + -1.6)(t + -1.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (t + -1.6) equal to 0.748331477 and -0.748331477.Subproblem 1
t + -1.6 = 0.748331477 Simplifying t + -1.6 = 0.748331477 Reorder the terms: -1.6 + t = 0.748331477 Solving -1.6 + t = 0.748331477 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + t = 0.748331477 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + t = 0.748331477 + 1.6 t = 0.748331477 + 1.6 Combine like terms: 0.748331477 + 1.6 = 2.348331477 t = 2.348331477 Simplifying t = 2.348331477Subproblem 2
t + -1.6 = -0.748331477 Simplifying t + -1.6 = -0.748331477 Reorder the terms: -1.6 + t = -0.748331477 Solving -1.6 + t = -0.748331477 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + t = -0.748331477 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + t = -0.748331477 + 1.6 t = -0.748331477 + 1.6 Combine like terms: -0.748331477 + 1.6 = 0.851668523 t = 0.851668523 Simplifying t = 0.851668523Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.348331477, 0.851668523}
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