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Simplifying 16t2 + 35t + 5 = 0 Reorder the terms: 5 + 35t + 16t2 = 0 Solving 5 + 35t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.3125 + 2.1875t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + 2.1875t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + 2.1875t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + 2.1875t + t2 = 0 + -0.3125 2.1875t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 2.1875t + t2 = -0.3125 The t term is 2.1875t. Take half its coefficient (1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. 2.1875t + 1.196289063 + t2 = -0.3125 + 1.196289063 Reorder the terms: 1.196289063 + 2.1875t + t2 = -0.3125 + 1.196289063 Combine like terms: -0.3125 + 1.196289063 = 0.883789063 1.196289063 + 2.1875t + t2 = 0.883789063 Factor a perfect square on the left side: (t + 1.09375)(t + 1.09375) = 0.883789063 Calculate the square root of the right side: 0.94010056 Break this problem into two subproblems by setting (t + 1.09375) equal to 0.94010056 and -0.94010056.Subproblem 1
t + 1.09375 = 0.94010056 Simplifying t + 1.09375 = 0.94010056 Reorder the terms: 1.09375 + t = 0.94010056 Solving 1.09375 + t = 0.94010056 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + t = 0.94010056 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + t = 0.94010056 + -1.09375 t = 0.94010056 + -1.09375 Combine like terms: 0.94010056 + -1.09375 = -0.15364944 t = -0.15364944 Simplifying t = -0.15364944Subproblem 2
t + 1.09375 = -0.94010056 Simplifying t + 1.09375 = -0.94010056 Reorder the terms: 1.09375 + t = -0.94010056 Solving 1.09375 + t = -0.94010056 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.09375' to each side of the equation. 1.09375 + -1.09375 + t = -0.94010056 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + t = -0.94010056 + -1.09375 t = -0.94010056 + -1.09375 Combine like terms: -0.94010056 + -1.09375 = -2.03385056 t = -2.03385056 Simplifying t = -2.03385056Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.15364944, -2.03385056}
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