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Simplifying 640(t) = -16t2 + 96t + 640 Reorder the terms: 640t = 640 + 96t + -16t2 Solving 640t = 640 + 96t + -16t2 Solving for variable 't'. Reorder the terms: -640 + 640t + -96t + 16t2 = 640 + 96t + -16t2 + -640 + -96t + 16t2 Combine like terms: 640t + -96t = 544t -640 + 544t + 16t2 = 640 + 96t + -16t2 + -640 + -96t + 16t2 Reorder the terms: -640 + 544t + 16t2 = 640 + -640 + 96t + -96t + -16t2 + 16t2 Combine like terms: 640 + -640 = 0 -640 + 544t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -640 + 544t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -640 + 544t + 16t2 = 0 + -16t2 + 16t2 -640 + 544t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -640 + 544t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-40 + 34t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-40 + 34t + t2)' equal to zero and attempt to solve: Simplifying -40 + 34t + t2 = 0 Solving -40 + 34t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 34t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + 34t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 34t + t2 = 0 + 40 34t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 34t + t2 = 40 The t term is 34t. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34t + 289 + t2 = 40 + 289 Reorder the terms: 289 + 34t + t2 = 40 + 289 Combine like terms: 40 + 289 = 329 289 + 34t + t2 = 329 Factor a perfect square on the left side: (t + 17)(t + 17) = 329 Calculate the square root of the right side: 18.138357147 Break this problem into two subproblems by setting (t + 17) equal to 18.138357147 and -18.138357147.Subproblem 1
t + 17 = 18.138357147 Simplifying t + 17 = 18.138357147 Reorder the terms: 17 + t = 18.138357147 Solving 17 + t = 18.138357147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + t = 18.138357147 + -17 Combine like terms: 17 + -17 = 0 0 + t = 18.138357147 + -17 t = 18.138357147 + -17 Combine like terms: 18.138357147 + -17 = 1.138357147 t = 1.138357147 Simplifying t = 1.138357147Subproblem 2
t + 17 = -18.138357147 Simplifying t + 17 = -18.138357147 Reorder the terms: 17 + t = -18.138357147 Solving 17 + t = -18.138357147 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + t = -18.138357147 + -17 Combine like terms: 17 + -17 = 0 0 + t = -18.138357147 + -17 t = -18.138357147 + -17 Combine like terms: -18.138357147 + -17 = -35.138357147 t = -35.138357147 Simplifying t = -35.138357147Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.138357147, -35.138357147}Solution
t = {1.138357147, -35.138357147}
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