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Simplifying 200 = -16t2 + 128t Reorder the terms: 200 = 128t + -16t2 Solving 200 = 128t + -16t2 Solving for variable 't'. Reorder the terms: 200 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2 Combine like terms: 128t + -128t = 0 200 + -128t + 16t2 = 0 + -16t2 + 16t2 200 + -128t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 200 + -128t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(25 + -16t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(25 + -16t + 2t2)' equal to zero and attempt to solve: Simplifying 25 + -16t + 2t2 = 0 Solving 25 + -16t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -8t + t2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -8t + -12.5 + t2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -8t + t2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -8t + t2 = 0 + -12.5 -8t + t2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -8t + t2 = -12.5 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -12.5 + 16 Reorder the terms: 16 + -8t + t2 = -12.5 + 16 Combine like terms: -12.5 + 16 = 3.5 16 + -8t + t2 = 3.5 Factor a perfect square on the left side: (t + -4)(t + -4) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (t + -4) equal to 1.870828693 and -1.870828693.Subproblem 1
t + -4 = 1.870828693 Simplifying t + -4 = 1.870828693 Reorder the terms: -4 + t = 1.870828693 Solving -4 + t = 1.870828693 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 1.870828693 + 4 Combine like terms: -4 + 4 = 0 0 + t = 1.870828693 + 4 t = 1.870828693 + 4 Combine like terms: 1.870828693 + 4 = 5.870828693 t = 5.870828693 Simplifying t = 5.870828693Subproblem 2
t + -4 = -1.870828693 Simplifying t + -4 = -1.870828693 Reorder the terms: -4 + t = -1.870828693 Solving -4 + t = -1.870828693 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -1.870828693 + 4 Combine like terms: -4 + 4 = 0 0 + t = -1.870828693 + 4 t = -1.870828693 + 4 Combine like terms: -1.870828693 + 4 = 2.129171307 t = 2.129171307 Simplifying t = 2.129171307Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.870828693, 2.129171307}Solution
t = {5.870828693, 2.129171307}
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