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Simplifying 43 = -16t2 + 64t + 512 Reorder the terms: 43 = 512 + 64t + -16t2 Solving 43 = 512 + 64t + -16t2 Solving for variable 't'. Combine like terms: 43 + -512 = -469 -469 + -64t + 16t2 = 512 + 64t + -16t2 + -512 + -64t + 16t2 Reorder the terms: -469 + -64t + 16t2 = 512 + -512 + 64t + -64t + -16t2 + 16t2 Combine like terms: 512 + -512 = 0 -469 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -469 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -469 + -64t + 16t2 = 0 + -16t2 + 16t2 -469 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -469 + -64t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -29.3125 + -4t + t2 = 0 Move the constant term to the right: Add '29.3125' to each side of the equation. -29.3125 + -4t + 29.3125 + t2 = 0 + 29.3125 Reorder the terms: -29.3125 + 29.3125 + -4t + t2 = 0 + 29.3125 Combine like terms: -29.3125 + 29.3125 = 0.0000 0.0000 + -4t + t2 = 0 + 29.3125 -4t + t2 = 0 + 29.3125 Combine like terms: 0 + 29.3125 = 29.3125 -4t + t2 = 29.3125 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 29.3125 + 4 Reorder the terms: 4 + -4t + t2 = 29.3125 + 4 Combine like terms: 29.3125 + 4 = 33.3125 4 + -4t + t2 = 33.3125 Factor a perfect square on the left side: (t + -2)(t + -2) = 33.3125 Calculate the square root of the right side: 5.77169819 Break this problem into two subproblems by setting (t + -2) equal to 5.77169819 and -5.77169819.Subproblem 1
t + -2 = 5.77169819 Simplifying t + -2 = 5.77169819 Reorder the terms: -2 + t = 5.77169819 Solving -2 + t = 5.77169819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 5.77169819 + 2 Combine like terms: -2 + 2 = 0 0 + t = 5.77169819 + 2 t = 5.77169819 + 2 Combine like terms: 5.77169819 + 2 = 7.77169819 t = 7.77169819 Simplifying t = 7.77169819Subproblem 2
t + -2 = -5.77169819 Simplifying t + -2 = -5.77169819 Reorder the terms: -2 + t = -5.77169819 Solving -2 + t = -5.77169819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -5.77169819 + 2 Combine like terms: -2 + 2 = 0 0 + t = -5.77169819 + 2 t = -5.77169819 + 2 Combine like terms: -5.77169819 + 2 = -3.77169819 t = -3.77169819 Simplifying t = -3.77169819Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.77169819, -3.77169819}
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