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Simplifying 0 = -16t2 + -16t + 9 Reorder the terms: 0 = 9 + -16t + -16t2 Solving 0 = 9 + -16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -9 = -9 -9 + 16t + 16t2 = 9 + -16t + -16t2 + -9 + 16t + 16t2 Reorder the terms: -9 + 16t + 16t2 = 9 + -9 + -16t + 16t + -16t2 + 16t2 Combine like terms: 9 + -9 = 0 -9 + 16t + 16t2 = 0 + -16t + 16t + -16t2 + 16t2 -9 + 16t + 16t2 = -16t + 16t + -16t2 + 16t2 Combine like terms: -16t + 16t = 0 -9 + 16t + 16t2 = 0 + -16t2 + 16t2 -9 + 16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -9 + 16t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t + t2 = 0 + 0.5625 t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 t + t2 = 0.5625 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 0.5625 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 0.5625 + 0.25 Combine like terms: 0.5625 + 0.25 = 0.8125 1.25 + t2 = 0.8125 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (t + 0.5) equal to 0.901387819 and -0.901387819.Subproblem 1
t + 0.5 = 0.901387819 Simplifying t + 0.5 = 0.901387819 Reorder the terms: 0.5 + t = 0.901387819 Solving 0.5 + t = 0.901387819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 0.901387819 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.901387819 + -0.5 t = 0.901387819 + -0.5 Combine like terms: 0.901387819 + -0.5 = 0.401387819 t = 0.401387819 Simplifying t = 0.401387819Subproblem 2
t + 0.5 = -0.901387819 Simplifying t + 0.5 = -0.901387819 Reorder the terms: 0.5 + t = -0.901387819 Solving 0.5 + t = -0.901387819 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -0.901387819 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.901387819 + -0.5 t = -0.901387819 + -0.5 Combine like terms: -0.901387819 + -0.5 = -1.401387819 t = -1.401387819 Simplifying t = -1.401387819Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.401387819, -1.401387819}
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