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Simplifying 16t2 + -35t + 7 = 25 Reorder the terms: 7 + -35t + 16t2 = 25 Solving 7 + -35t + 16t2 = 25 Solving for variable 't'. Reorder the terms: 7 + -25 + -35t + 16t2 = 25 + -25 Combine like terms: 7 + -25 = -18 -18 + -35t + 16t2 = 25 + -25 Combine like terms: 25 + -25 = 0 -18 + -35t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.125 + -2.1875t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -2.1875t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -2.1875t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -2.1875t + t2 = 0 + 1.125 -2.1875t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -2.1875t + t2 = 1.125 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 = 1.125 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = 1.125 + 1.196289063 Combine like terms: 1.125 + 1.196289063 = 2.321289063 1.196289063 + -2.1875t + t2 = 2.321289063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 2.321289063 Calculate the square root of the right side: 1.523577718 Break this problem into two subproblems by setting (t + -1.09375) equal to 1.523577718 and -1.523577718.Subproblem 1
t + -1.09375 = 1.523577718 Simplifying t + -1.09375 = 1.523577718 Reorder the terms: -1.09375 + t = 1.523577718 Solving -1.09375 + t = 1.523577718 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 = 1.523577718 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 1.523577718 + 1.09375 t = 1.523577718 + 1.09375 Combine like terms: 1.523577718 + 1.09375 = 2.617327718 t = 2.617327718 Simplifying t = 2.617327718Subproblem 2
t + -1.09375 = -1.523577718 Simplifying t + -1.09375 = -1.523577718 Reorder the terms: -1.09375 + t = -1.523577718 Solving -1.09375 + t = -1.523577718 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 = -1.523577718 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -1.523577718 + 1.09375 t = -1.523577718 + 1.09375 Combine like terms: -1.523577718 + 1.09375 = -0.429827718 t = -0.429827718 Simplifying t = -0.429827718Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.617327718, -0.429827718}
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