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Simplifying 0.1 = -16t2 + 4t + 2 Reorder the terms: 0.1 = 2 + 4t + -16t2 Solving 0.1 = 2 + 4t + -16t2 Solving for variable 't'. Combine like terms: 0.1 + -2 = -1.9 -1.9 + -4t + 16t2 = 2 + 4t + -16t2 + -2 + -4t + 16t2 Reorder the terms: -1.9 + -4t + 16t2 = 2 + -2 + 4t + -4t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -1.9 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -1.9 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -1.9 + -4t + 16t2 = 0 + -16t2 + 16t2 -1.9 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1.9 + -4t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.11875 + -0.25t + t2 = 0 Move the constant term to the right: Add '0.11875' to each side of the equation. -0.11875 + -0.25t + 0.11875 + t2 = 0 + 0.11875 Reorder the terms: -0.11875 + 0.11875 + -0.25t + t2 = 0 + 0.11875 Combine like terms: -0.11875 + 0.11875 = 0.00000 0.00000 + -0.25t + t2 = 0 + 0.11875 -0.25t + t2 = 0 + 0.11875 Combine like terms: 0 + 0.11875 = 0.11875 -0.25t + t2 = 0.11875 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 0.11875 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 0.11875 + 0.015625 Combine like terms: 0.11875 + 0.015625 = 0.134375 0.015625 + -0.25t + t2 = 0.134375 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 0.134375 Calculate the square root of the right side: 0.366571957 Break this problem into two subproblems by setting (t + -0.125) equal to 0.366571957 and -0.366571957.Subproblem 1
t + -0.125 = 0.366571957 Simplifying t + -0.125 = 0.366571957 Reorder the terms: -0.125 + t = 0.366571957 Solving -0.125 + t = 0.366571957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 0.366571957 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 0.366571957 + 0.125 t = 0.366571957 + 0.125 Combine like terms: 0.366571957 + 0.125 = 0.491571957 t = 0.491571957 Simplifying t = 0.491571957Subproblem 2
t + -0.125 = -0.366571957 Simplifying t + -0.125 = -0.366571957 Reorder the terms: -0.125 + t = -0.366571957 Solving -0.125 + t = -0.366571957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -0.366571957 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -0.366571957 + 0.125 t = -0.366571957 + 0.125 Combine like terms: -0.366571957 + 0.125 = -0.241571957 t = -0.241571957 Simplifying t = -0.241571957Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.491571957, -0.241571957}
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