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Simplifying 20 = 16t2 + 35t + 2 Reorder the terms: 20 = 2 + 35t + 16t2 Solving 20 = 2 + 35t + 16t2 Solving for variable 't'. Combine like terms: 20 + -2 = 18 18 + -35t + -16t2 = 2 + 35t + 16t2 + -2 + -35t + -16t2 Reorder the terms: 18 + -35t + -16t2 = 2 + -2 + 35t + -35t + 16t2 + -16t2 Combine like terms: 2 + -2 = 0 18 + -35t + -16t2 = 0 + 35t + -35t + 16t2 + -16t2 18 + -35t + -16t2 = 35t + -35t + 16t2 + -16t2 Combine like terms: 35t + -35t = 0 18 + -35t + -16t2 = 0 + 16t2 + -16t2 18 + -35t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 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 = 0.429827718 t = 0.429827718 Simplifying t = 0.429827718Subproblem 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 = -2.617327718 t = -2.617327718 Simplifying t = -2.617327718Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.429827718, -2.617327718}
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