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Simplifying t = -16t2 + 80t + 4 Reorder the terms: t = 4 + 80t + -16t2 Solving t = 4 + 80t + -16t2 Solving for variable 't'. Reorder the terms: -4 + t + -80t + 16t2 = 4 + 80t + -16t2 + -4 + -80t + 16t2 Combine like terms: t + -80t = -79t -4 + -79t + 16t2 = 4 + 80t + -16t2 + -4 + -80t + 16t2 Reorder the terms: -4 + -79t + 16t2 = 4 + -4 + 80t + -80t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -79t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2 -4 + -79t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 -4 + -79t + 16t2 = 0 + -16t2 + 16t2 -4 + -79t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -79t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -4.9375t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4.9375t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4.9375t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4.9375t + t2 = 0 + 0.25 -4.9375t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4.9375t + t2 = 0.25 The t term is -4.9375t. Take half its coefficient (-2.46875). Square it (6.094726563) and add it to both sides. Add '6.094726563' to each side of the equation. -4.9375t + 6.094726563 + t2 = 0.25 + 6.094726563 Reorder the terms: 6.094726563 + -4.9375t + t2 = 0.25 + 6.094726563 Combine like terms: 0.25 + 6.094726563 = 6.344726563 6.094726563 + -4.9375t + t2 = 6.344726563 Factor a perfect square on the left side: (t + -2.46875)(t + -2.46875) = 6.344726563 Calculate the square root of the right side: 2.518874067 Break this problem into two subproblems by setting (t + -2.46875) equal to 2.518874067 and -2.518874067.Subproblem 1
t + -2.46875 = 2.518874067 Simplifying t + -2.46875 = 2.518874067 Reorder the terms: -2.46875 + t = 2.518874067 Solving -2.46875 + t = 2.518874067 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.46875' to each side of the equation. -2.46875 + 2.46875 + t = 2.518874067 + 2.46875 Combine like terms: -2.46875 + 2.46875 = 0.00000 0.00000 + t = 2.518874067 + 2.46875 t = 2.518874067 + 2.46875 Combine like terms: 2.518874067 + 2.46875 = 4.987624067 t = 4.987624067 Simplifying t = 4.987624067Subproblem 2
t + -2.46875 = -2.518874067 Simplifying t + -2.46875 = -2.518874067 Reorder the terms: -2.46875 + t = -2.518874067 Solving -2.46875 + t = -2.518874067 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.46875' to each side of the equation. -2.46875 + 2.46875 + t = -2.518874067 + 2.46875 Combine like terms: -2.46875 + 2.46875 = 0.00000 0.00000 + t = -2.518874067 + 2.46875 t = -2.518874067 + 2.46875 Combine like terms: -2.518874067 + 2.46875 = -0.050124067 t = -0.050124067 Simplifying t = -0.050124067Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.987624067, -0.050124067}
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