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Simplifying -16t2 + 35t = 16 Reorder the terms: 35t + -16t2 = 16 Solving 35t + -16t2 = 16 Solving for variable 't'. Reorder the terms: -16 + 35t + -16t2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 35t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1 + -2.1875t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.1875t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -2.1875t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.1875t + t2 = 0 + -1 -2.1875t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.1875t + t2 = -1 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 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = -1 + 1.196289063 Combine like terms: -1 + 1.196289063 = 0.196289063 1.196289063 + -2.1875t + t2 = 0.196289063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 0.196289063 Calculate the square root of the right side: 0.443045216 Break this problem into two subproblems by setting (t + -1.09375) equal to 0.443045216 and -0.443045216.Subproblem 1
t + -1.09375 = 0.443045216 Simplifying t + -1.09375 = 0.443045216 Reorder the terms: -1.09375 + t = 0.443045216 Solving -1.09375 + t = 0.443045216 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 = 0.443045216 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 0.443045216 + 1.09375 t = 0.443045216 + 1.09375 Combine like terms: 0.443045216 + 1.09375 = 1.536795216 t = 1.536795216 Simplifying t = 1.536795216Subproblem 2
t + -1.09375 = -0.443045216 Simplifying t + -1.09375 = -0.443045216 Reorder the terms: -1.09375 + t = -0.443045216 Solving -1.09375 + t = -0.443045216 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 = -0.443045216 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -0.443045216 + 1.09375 t = -0.443045216 + 1.09375 Combine like terms: -0.443045216 + 1.09375 = 0.650704784 t = 0.650704784 Simplifying t = 0.650704784Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.536795216, 0.650704784}
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