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Simplifying 0 = -16t2 + 16t + 1200 Reorder the terms: 0 = 1200 + 16t + -16t2 Solving 0 = 1200 + 16t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1200 = -1200 -1200 + -16t + 16t2 = 1200 + 16t + -16t2 + -1200 + -16t + 16t2 Reorder the terms: -1200 + -16t + 16t2 = 1200 + -1200 + 16t + -16t + -16t2 + 16t2 Combine like terms: 1200 + -1200 = 0 -1200 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2 -1200 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2 Combine like terms: 16t + -16t = 0 -1200 + -16t + 16t2 = 0 + -16t2 + 16t2 -1200 + -16t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1200 + -16t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-75 + -1t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-75 + -1t + t2)' equal to zero and attempt to solve: Simplifying -75 + -1t + t2 = 0 Solving -75 + -1t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + -1t + 75 + t2 = 0 + 75 Reorder the terms: -75 + 75 + -1t + t2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -1t + t2 = 0 + 75 -1t + t2 = 0 + 75 Combine like terms: 0 + 75 = 75 -1t + t2 = 75 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 75 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 75 + 0.25 Combine like terms: 75 + 0.25 = 75.25 0.25 + -1t + t2 = 75.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (t + -0.5) equal to 8.674675786 and -8.674675786.Subproblem 1
t + -0.5 = 8.674675786 Simplifying t + -0.5 = 8.674675786 Reorder the terms: -0.5 + t = 8.674675786 Solving -0.5 + t = 8.674675786 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 8.674675786 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 8.674675786 + 0.5 t = 8.674675786 + 0.5 Combine like terms: 8.674675786 + 0.5 = 9.174675786 t = 9.174675786 Simplifying t = 9.174675786Subproblem 2
t + -0.5 = -8.674675786 Simplifying t + -0.5 = -8.674675786 Reorder the terms: -0.5 + t = -8.674675786 Solving -0.5 + t = -8.674675786 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -8.674675786 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -8.674675786 + 0.5 t = -8.674675786 + 0.5 Combine like terms: -8.674675786 + 0.5 = -8.174675786 t = -8.174675786 Simplifying t = -8.174675786Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.174675786, -8.174675786}Solution
t = {9.174675786, -8.174675786}
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