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Simplifying -16t2 + 35t + 4 = 0 Reorder the terms: 4 + 35t + -16t2 = 0 Solving 4 + 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'. -0.25 + -2.1875t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.1875t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.1875t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.1875t + t2 = 0 + 0.25 -2.1875t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.1875t + t2 = 0.25 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 = 0.25 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = 0.25 + 1.196289063 Combine like terms: 0.25 + 1.196289063 = 1.446289063 1.196289063 + -2.1875t + t2 = 1.446289063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 1.446289063 Calculate the square root of the right side: 1.202617588 Break this problem into two subproblems by setting (t + -1.09375) equal to 1.202617588 and -1.202617588.Subproblem 1
t + -1.09375 = 1.202617588 Simplifying t + -1.09375 = 1.202617588 Reorder the terms: -1.09375 + t = 1.202617588 Solving -1.09375 + t = 1.202617588 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 = 1.202617588 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 1.202617588 + 1.09375 t = 1.202617588 + 1.09375 Combine like terms: 1.202617588 + 1.09375 = 2.296367588 t = 2.296367588 Simplifying t = 2.296367588Subproblem 2
t + -1.09375 = -1.202617588 Simplifying t + -1.09375 = -1.202617588 Reorder the terms: -1.09375 + t = -1.202617588 Solving -1.09375 + t = -1.202617588 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 = -1.202617588 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -1.202617588 + 1.09375 t = -1.202617588 + 1.09375 Combine like terms: -1.202617588 + 1.09375 = -0.108867588 t = -0.108867588 Simplifying t = -0.108867588Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.296367588, -0.108867588}
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