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Simplifying 64t2 + 14t + -1.853539666 = 0 Reorder the terms: -1.853539666 + 14t + 64t2 = 0 Solving -1.853539666 + 14t + 64t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.02896155728 + 0.21875t + t2 = 0 Move the constant term to the right: Add '0.02896155728' to each side of the equation. -0.02896155728 + 0.21875t + 0.02896155728 + t2 = 0 + 0.02896155728 Reorder the terms: -0.02896155728 + 0.02896155728 + 0.21875t + t2 = 0 + 0.02896155728 Combine like terms: -0.02896155728 + 0.02896155728 = 0.00000000000 0.00000000000 + 0.21875t + t2 = 0 + 0.02896155728 0.21875t + t2 = 0 + 0.02896155728 Combine like terms: 0 + 0.02896155728 = 0.02896155728 0.21875t + t2 = 0.02896155728 The t term is 0.21875t. Take half its coefficient (0.109375). Square it (0.01196289063) and add it to both sides. Add '0.01196289063' to each side of the equation. 0.21875t + 0.01196289063 + t2 = 0.02896155728 + 0.01196289063 Reorder the terms: 0.01196289063 + 0.21875t + t2 = 0.02896155728 + 0.01196289063 Combine like terms: 0.02896155728 + 0.01196289063 = 0.04092444791 0.01196289063 + 0.21875t + t2 = 0.04092444791 Factor a perfect square on the left side: (t + 0.109375)(t + 0.109375) = 0.04092444791 Calculate the square root of the right side: 0.202297919 Break this problem into two subproblems by setting (t + 0.109375) equal to 0.202297919 and -0.202297919.Subproblem 1
t + 0.109375 = 0.202297919 Simplifying t + 0.109375 = 0.202297919 Reorder the terms: 0.109375 + t = 0.202297919 Solving 0.109375 + t = 0.202297919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.109375' to each side of the equation. 0.109375 + -0.109375 + t = 0.202297919 + -0.109375 Combine like terms: 0.109375 + -0.109375 = 0.000000 0.000000 + t = 0.202297919 + -0.109375 t = 0.202297919 + -0.109375 Combine like terms: 0.202297919 + -0.109375 = 0.092922919 t = 0.092922919 Simplifying t = 0.092922919Subproblem 2
t + 0.109375 = -0.202297919 Simplifying t + 0.109375 = -0.202297919 Reorder the terms: 0.109375 + t = -0.202297919 Solving 0.109375 + t = -0.202297919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.109375' to each side of the equation. 0.109375 + -0.109375 + t = -0.202297919 + -0.109375 Combine like terms: 0.109375 + -0.109375 = 0.000000 0.000000 + t = -0.202297919 + -0.109375 t = -0.202297919 + -0.109375 Combine like terms: -0.202297919 + -0.109375 = -0.311672919 t = -0.311672919 Simplifying t = -0.311672919Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.092922919, -0.311672919}
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