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Simplifying -16t2 + 96t + 640 = t Reorder the terms: 640 + 96t + -16t2 = t Solving 640 + 96t + -16t2 = t Solving for variable 't'. Reorder the terms: 640 + 96t + -1t + -16t2 = t + -1t Combine like terms: 96t + -1t = 95t 640 + 95t + -16t2 = t + -1t Combine like terms: t + -1t = 0 640 + 95t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -40 + -5.9375t + t2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -5.9375t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + -5.9375t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -5.9375t + t2 = 0 + 40 -5.9375t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 -5.9375t + t2 = 40 The t term is -5.9375t. Take half its coefficient (-2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. -5.9375t + 8.813476563 + t2 = 40 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375t + t2 = 40 + 8.813476563 Combine like terms: 40 + 8.813476563 = 48.813476563 8.813476563 + -5.9375t + t2 = 48.813476563 Factor a perfect square on the left side: (t + -2.96875)(t + -2.96875) = 48.813476563 Calculate the square root of the right side: 6.986664194 Break this problem into two subproblems by setting (t + -2.96875) equal to 6.986664194 and -6.986664194.Subproblem 1
t + -2.96875 = 6.986664194 Simplifying t + -2.96875 = 6.986664194 Reorder the terms: -2.96875 + t = 6.986664194 Solving -2.96875 + t = 6.986664194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + t = 6.986664194 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = 6.986664194 + 2.96875 t = 6.986664194 + 2.96875 Combine like terms: 6.986664194 + 2.96875 = 9.955414194 t = 9.955414194 Simplifying t = 9.955414194Subproblem 2
t + -2.96875 = -6.986664194 Simplifying t + -2.96875 = -6.986664194 Reorder the terms: -2.96875 + t = -6.986664194 Solving -2.96875 + t = -6.986664194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + t = -6.986664194 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = -6.986664194 + 2.96875 t = -6.986664194 + 2.96875 Combine like terms: -6.986664194 + 2.96875 = -4.017914194 t = -4.017914194 Simplifying t = -4.017914194Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.955414194, -4.017914194}
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