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Simplifying 0 = -16t2 + 32t + 3 Reorder the terms: 0 = 3 + 32t + -16t2 Solving 0 = 3 + 32t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -32t + 16t2 = 3 + 32t + -16t2 + -3 + -32t + 16t2 Reorder the terms: -3 + -32t + 16t2 = 3 + -3 + 32t + -32t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 -3 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -3 + -32t + 16t2 = 0 + -16t2 + 16t2 -3 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -32t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -2t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -2t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -2t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -2t + t2 = 0 + 0.1875 -2t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -2t + t2 = 0.1875 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 = 0.1875 + 1 Reorder the terms: 1 + -2t + t2 = 0.1875 + 1 Combine like terms: 0.1875 + 1 = 1.1875 1 + -2t + t2 = 1.1875 Factor a perfect square on the left side: (t + -1)(t + -1) = 1.1875 Calculate the square root of the right side: 1.089724736 Break this problem into two subproblems by setting (t + -1) equal to 1.089724736 and -1.089724736.Subproblem 1
t + -1 = 1.089724736 Simplifying t + -1 = 1.089724736 Reorder the terms: -1 + t = 1.089724736 Solving -1 + t = 1.089724736 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 = 1.089724736 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.089724736 + 1 t = 1.089724736 + 1 Combine like terms: 1.089724736 + 1 = 2.089724736 t = 2.089724736 Simplifying t = 2.089724736Subproblem 2
t + -1 = -1.089724736 Simplifying t + -1 = -1.089724736 Reorder the terms: -1 + t = -1.089724736 Solving -1 + t = -1.089724736 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 = -1.089724736 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.089724736 + 1 t = -1.089724736 + 1 Combine like terms: -1.089724736 + 1 = -0.089724736 t = -0.089724736 Simplifying t = -0.089724736Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.089724736, -0.089724736}
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