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Simplifying -0.075 = -16t2 + 2.4t Reorder the terms: -0.075 = 2.4t + -16t2 Solving -0.075 = 2.4t + -16t2 Solving for variable 't'. Reorder the terms: -0.075 + -2.4t + 16t2 = 2.4t + -2.4t + -16t2 + 16t2 Combine like terms: 2.4t + -2.4t = 0.0 -0.075 + -2.4t + 16t2 = 0.0 + -16t2 + 16t2 -0.075 + -2.4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -0.075 + -2.4t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0046875 + -0.15t + t2 = 0 Move the constant term to the right: Add '0.0046875' to each side of the equation. -0.0046875 + -0.15t + 0.0046875 + t2 = 0 + 0.0046875 Reorder the terms: -0.0046875 + 0.0046875 + -0.15t + t2 = 0 + 0.0046875 Combine like terms: -0.0046875 + 0.0046875 = 0.0000000 0.0000000 + -0.15t + t2 = 0 + 0.0046875 -0.15t + t2 = 0 + 0.0046875 Combine like terms: 0 + 0.0046875 = 0.0046875 -0.15t + t2 = 0.0046875 The t term is -0.15t. Take half its coefficient (-0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. -0.15t + 0.005625 + t2 = 0.0046875 + 0.005625 Reorder the terms: 0.005625 + -0.15t + t2 = 0.0046875 + 0.005625 Combine like terms: 0.0046875 + 0.005625 = 0.0103125 0.005625 + -0.15t + t2 = 0.0103125 Factor a perfect square on the left side: (t + -0.075)(t + -0.075) = 0.0103125 Calculate the square root of the right side: 0.10155048 Break this problem into two subproblems by setting (t + -0.075) equal to 0.10155048 and -0.10155048.Subproblem 1
t + -0.075 = 0.10155048 Simplifying t + -0.075 = 0.10155048 Reorder the terms: -0.075 + t = 0.10155048 Solving -0.075 + t = 0.10155048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + t = 0.10155048 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + t = 0.10155048 + 0.075 t = 0.10155048 + 0.075 Combine like terms: 0.10155048 + 0.075 = 0.17655048 t = 0.17655048 Simplifying t = 0.17655048Subproblem 2
t + -0.075 = -0.10155048 Simplifying t + -0.075 = -0.10155048 Reorder the terms: -0.075 + t = -0.10155048 Solving -0.075 + t = -0.10155048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + t = -0.10155048 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + t = -0.10155048 + 0.075 t = -0.10155048 + 0.075 Combine like terms: -0.10155048 + 0.075 = -0.02655048 t = -0.02655048 Simplifying t = -0.02655048Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.17655048, -0.02655048}
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