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Simplifying 0.1 = -16t2 + 8t + 2 Reorder the terms: 0.1 = 2 + 8t + -16t2 Solving 0.1 = 2 + 8t + -16t2 Solving for variable 't'. Combine like terms: 0.1 + -2 = -1.9 -1.9 + -8t + 16t2 = 2 + 8t + -16t2 + -2 + -8t + 16t2 Reorder the terms: -1.9 + -8t + 16t2 = 2 + -2 + 8t + -8t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -1.9 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2 -1.9 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2 Combine like terms: 8t + -8t = 0 -1.9 + -8t + 16t2 = 0 + -16t2 + 16t2 -1.9 + -8t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1.9 + -8t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.11875 + -0.5t + t2 = 0 Move the constant term to the right: Add '0.11875' to each side of the equation. -0.11875 + -0.5t + 0.11875 + t2 = 0 + 0.11875 Reorder the terms: -0.11875 + 0.11875 + -0.5t + t2 = 0 + 0.11875 Combine like terms: -0.11875 + 0.11875 = 0.00000 0.00000 + -0.5t + t2 = 0 + 0.11875 -0.5t + t2 = 0 + 0.11875 Combine like terms: 0 + 0.11875 = 0.11875 -0.5t + t2 = 0.11875 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 0.11875 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 0.11875 + 0.0625 Combine like terms: 0.11875 + 0.0625 = 0.18125 0.0625 + -0.5t + t2 = 0.18125 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 0.18125 Calculate the square root of the right side: 0.425734659 Break this problem into two subproblems by setting (t + -0.25) equal to 0.425734659 and -0.425734659.Subproblem 1
t + -0.25 = 0.425734659 Simplifying t + -0.25 = 0.425734659 Reorder the terms: -0.25 + t = 0.425734659 Solving -0.25 + t = 0.425734659 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 0.425734659 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 0.425734659 + 0.25 t = 0.425734659 + 0.25 Combine like terms: 0.425734659 + 0.25 = 0.675734659 t = 0.675734659 Simplifying t = 0.675734659Subproblem 2
t + -0.25 = -0.425734659 Simplifying t + -0.25 = -0.425734659 Reorder the terms: -0.25 + t = -0.425734659 Solving -0.25 + t = -0.425734659 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -0.425734659 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -0.425734659 + 0.25 t = -0.425734659 + 0.25 Combine like terms: -0.425734659 + 0.25 = -0.175734659 t = -0.175734659 Simplifying t = -0.175734659Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.675734659, -0.175734659}
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