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Simplifying 0 = -16t2 + 120t + 250 Reorder the terms: 0 = 250 + 120t + -16t2 Solving 0 = 250 + 120t + -16t2 Solving for variable 't'. Combine like terms: 0 + -250 = -250 -250 + -120t + 16t2 = 250 + 120t + -16t2 + -250 + -120t + 16t2 Reorder the terms: -250 + -120t + 16t2 = 250 + -250 + 120t + -120t + -16t2 + 16t2 Combine like terms: 250 + -250 = 0 -250 + -120t + 16t2 = 0 + 120t + -120t + -16t2 + 16t2 -250 + -120t + 16t2 = 120t + -120t + -16t2 + 16t2 Combine like terms: 120t + -120t = 0 -250 + -120t + 16t2 = 0 + -16t2 + 16t2 -250 + -120t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -250 + -120t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-125 + -60t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-125 + -60t + 8t2)' equal to zero and attempt to solve: Simplifying -125 + -60t + 8t2 = 0 Solving -125 + -60t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15.625 + -7.5t + t2 = 0 Move the constant term to the right: Add '15.625' to each side of the equation. -15.625 + -7.5t + 15.625 + t2 = 0 + 15.625 Reorder the terms: -15.625 + 15.625 + -7.5t + t2 = 0 + 15.625 Combine like terms: -15.625 + 15.625 = 0.000 0.000 + -7.5t + t2 = 0 + 15.625 -7.5t + t2 = 0 + 15.625 Combine like terms: 0 + 15.625 = 15.625 -7.5t + t2 = 15.625 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = 15.625 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = 15.625 + 14.0625 Combine like terms: 15.625 + 14.0625 = 29.6875 14.0625 + -7.5t + t2 = 29.6875 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 29.6875 Calculate the square root of the right side: 5.448623679 Break this problem into two subproblems by setting (t + -3.75) equal to 5.448623679 and -5.448623679.Subproblem 1
t + -3.75 = 5.448623679 Simplifying t + -3.75 = 5.448623679 Reorder the terms: -3.75 + t = 5.448623679 Solving -3.75 + t = 5.448623679 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 5.448623679 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 5.448623679 + 3.75 t = 5.448623679 + 3.75 Combine like terms: 5.448623679 + 3.75 = 9.198623679 t = 9.198623679 Simplifying t = 9.198623679Subproblem 2
t + -3.75 = -5.448623679 Simplifying t + -3.75 = -5.448623679 Reorder the terms: -3.75 + t = -5.448623679 Solving -3.75 + t = -5.448623679 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -5.448623679 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -5.448623679 + 3.75 t = -5.448623679 + 3.75 Combine like terms: -5.448623679 + 3.75 = -1.698623679 t = -1.698623679 Simplifying t = -1.698623679Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.198623679, -1.698623679}Solution
t = {9.198623679, -1.698623679}
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