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Simplifying 16(t2 + -1600t + 900) = 0 Reorder the terms: 16(900 + -1600t + t2) = 0 (900 * 16 + -1600t * 16 + t2 * 16) = 0 (14400 + -25600t + 16t2) = 0 Solving 14400 + -25600t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(900 + -1600t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(900 + -1600t + t2)' equal to zero and attempt to solve: Simplifying 900 + -1600t + t2 = 0 Solving 900 + -1600t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-900' to each side of the equation. 900 + -1600t + -900 + t2 = 0 + -900 Reorder the terms: 900 + -900 + -1600t + t2 = 0 + -900 Combine like terms: 900 + -900 = 0 0 + -1600t + t2 = 0 + -900 -1600t + t2 = 0 + -900 Combine like terms: 0 + -900 = -900 -1600t + t2 = -900 The t term is -1600t. Take half its coefficient (-800). Square it (640000) and add it to both sides. Add '640000' to each side of the equation. -1600t + 640000 + t2 = -900 + 640000 Reorder the terms: 640000 + -1600t + t2 = -900 + 640000 Combine like terms: -900 + 640000 = 639100 640000 + -1600t + t2 = 639100 Factor a perfect square on the left side: (t + -800)(t + -800) = 639100 Calculate the square root of the right side: 799.437302107 Break this problem into two subproblems by setting (t + -800) equal to 799.437302107 and -799.437302107.Subproblem 1
t + -800 = 799.437302107 Simplifying t + -800 = 799.437302107 Reorder the terms: -800 + t = 799.437302107 Solving -800 + t = 799.437302107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '800' to each side of the equation. -800 + 800 + t = 799.437302107 + 800 Combine like terms: -800 + 800 = 0 0 + t = 799.437302107 + 800 t = 799.437302107 + 800 Combine like terms: 799.437302107 + 800 = 1599.437302107 t = 1599.437302107 Simplifying t = 1599.437302107Subproblem 2
t + -800 = -799.437302107 Simplifying t + -800 = -799.437302107 Reorder the terms: -800 + t = -799.437302107 Solving -800 + t = -799.437302107 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '800' to each side of the equation. -800 + 800 + t = -799.437302107 + 800 Combine like terms: -800 + 800 = 0 0 + t = -799.437302107 + 800 t = -799.437302107 + 800 Combine like terms: -799.437302107 + 800 = 0.562697893 t = 0.562697893 Simplifying t = 0.562697893Solution
The solution to the problem is based on the solutions from the subproblems. t = {1599.437302107, 0.562697893}Solution
t = {1599.437302107, 0.562697893}
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