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Simplifying -16t2 + 96t + 5 = t Reorder the terms: 5 + 96t + -16t2 = t Solving 5 + 96t + -16t2 = t Solving for variable 't'. Reorder the terms: 5 + 96t + -1t + -16t2 = t + -1t Combine like terms: 96t + -1t = 95t 5 + 95t + -16t2 = t + -1t Combine like terms: t + -1t = 0 5 + 95t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -5.9375t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -5.9375t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -5.9375t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -5.9375t + t2 = 0 + 0.3125 -5.9375t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -5.9375t + t2 = 0.3125 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 = 0.3125 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375t + t2 = 0.3125 + 8.813476563 Combine like terms: 0.3125 + 8.813476563 = 9.125976563 8.813476563 + -5.9375t + t2 = 9.125976563 Factor a perfect square on the left side: (t + -2.96875)(t + -2.96875) = 9.125976563 Calculate the square root of the right side: 3.020923131 Break this problem into two subproblems by setting (t + -2.96875) equal to 3.020923131 and -3.020923131.Subproblem 1
t + -2.96875 = 3.020923131 Simplifying t + -2.96875 = 3.020923131 Reorder the terms: -2.96875 + t = 3.020923131 Solving -2.96875 + t = 3.020923131 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 = 3.020923131 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = 3.020923131 + 2.96875 t = 3.020923131 + 2.96875 Combine like terms: 3.020923131 + 2.96875 = 5.989673131 t = 5.989673131 Simplifying t = 5.989673131Subproblem 2
t + -2.96875 = -3.020923131 Simplifying t + -2.96875 = -3.020923131 Reorder the terms: -2.96875 + t = -3.020923131 Solving -2.96875 + t = -3.020923131 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 = -3.020923131 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = -3.020923131 + 2.96875 t = -3.020923131 + 2.96875 Combine like terms: -3.020923131 + 2.96875 = -0.052173131 t = -0.052173131 Simplifying t = -0.052173131Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.989673131, -0.052173131}
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