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Simplifying -16t2 + -35t + 3 = 0 Reorder the terms: 3 + -35t + -16t2 = 0 Solving 3 + -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'. -0.1875 + 2.1875t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 2.1875t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 2.1875t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 2.1875t + t2 = 0 + 0.1875 2.1875t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 2.1875t + t2 = 0.1875 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 = 0.1875 + 1.196289063 Reorder the terms: 1.196289063 + 2.1875t + t2 = 0.1875 + 1.196289063 Combine like terms: 0.1875 + 1.196289063 = 1.383789063 1.196289063 + 2.1875t + t2 = 1.383789063 Factor a perfect square on the left side: (t + 1.09375)(t + 1.09375) = 1.383789063 Calculate the square root of the right side: 1.176345639 Break this problem into two subproblems by setting (t + 1.09375) equal to 1.176345639 and -1.176345639.Subproblem 1
t + 1.09375 = 1.176345639 Simplifying t + 1.09375 = 1.176345639 Reorder the terms: 1.09375 + t = 1.176345639 Solving 1.09375 + t = 1.176345639 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 = 1.176345639 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + t = 1.176345639 + -1.09375 t = 1.176345639 + -1.09375 Combine like terms: 1.176345639 + -1.09375 = 0.082595639 t = 0.082595639 Simplifying t = 0.082595639Subproblem 2
t + 1.09375 = -1.176345639 Simplifying t + 1.09375 = -1.176345639 Reorder the terms: 1.09375 + t = -1.176345639 Solving 1.09375 + t = -1.176345639 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 = -1.176345639 + -1.09375 Combine like terms: 1.09375 + -1.09375 = 0.00000 0.00000 + t = -1.176345639 + -1.09375 t = -1.176345639 + -1.09375 Combine like terms: -1.176345639 + -1.09375 = -2.270095639 t = -2.270095639 Simplifying t = -2.270095639Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.082595639, -2.270095639}
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