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Simplifying 0 = -16t2 + 104t + 60 Reorder the terms: 0 = 60 + 104t + -16t2 Solving 0 = 60 + 104t + -16t2 Solving for variable 't'. Combine like terms: 0 + -60 = -60 -60 + -104t + 16t2 = 60 + 104t + -16t2 + -60 + -104t + 16t2 Reorder the terms: -60 + -104t + 16t2 = 60 + -60 + 104t + -104t + -16t2 + 16t2 Combine like terms: 60 + -60 = 0 -60 + -104t + 16t2 = 0 + 104t + -104t + -16t2 + 16t2 -60 + -104t + 16t2 = 104t + -104t + -16t2 + 16t2 Combine like terms: 104t + -104t = 0 -60 + -104t + 16t2 = 0 + -16t2 + 16t2 -60 + -104t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -60 + -104t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -26t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -26t + 4t2)' equal to zero and attempt to solve: Simplifying -15 + -26t + 4t2 = 0 Solving -15 + -26t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -6.5t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -6.5t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -6.5t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -6.5t + t2 = 0 + 3.75 -6.5t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -6.5t + t2 = 3.75 The t term is -6.5t. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5t + 10.5625 + t2 = 3.75 + 10.5625 Reorder the terms: 10.5625 + -6.5t + t2 = 3.75 + 10.5625 Combine like terms: 3.75 + 10.5625 = 14.3125 10.5625 + -6.5t + t2 = 14.3125 Factor a perfect square on the left side: (t + -3.25)(t + -3.25) = 14.3125 Calculate the square root of the right side: 3.783186488 Break this problem into two subproblems by setting (t + -3.25) equal to 3.783186488 and -3.783186488.Subproblem 1
t + -3.25 = 3.783186488 Simplifying t + -3.25 = 3.783186488 Reorder the terms: -3.25 + t = 3.783186488 Solving -3.25 + t = 3.783186488 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + t = 3.783186488 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + t = 3.783186488 + 3.25 t = 3.783186488 + 3.25 Combine like terms: 3.783186488 + 3.25 = 7.033186488 t = 7.033186488 Simplifying t = 7.033186488Subproblem 2
t + -3.25 = -3.783186488 Simplifying t + -3.25 = -3.783186488 Reorder the terms: -3.25 + t = -3.783186488 Solving -3.25 + t = -3.783186488 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + t = -3.783186488 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + t = -3.783186488 + 3.25 t = -3.783186488 + 3.25 Combine like terms: -3.783186488 + 3.25 = -0.533186488 t = -0.533186488 Simplifying t = -0.533186488Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.033186488, -0.533186488}Solution
t = {7.033186488, -0.533186488}
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