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Simplifying -16t2 + 38.4t + 3.5 = 0 Reorder the terms: 3.5 + 38.4t + -16t2 = 0 Solving 3.5 + 38.4t + -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'. -0.21875 + -2.4t + t2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + -2.4t + 0.21875 + t2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + -2.4t + t2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + -2.4t + t2 = 0 + 0.21875 -2.4t + t2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 -2.4t + t2 = 0.21875 The t term is -2.4t. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4t + 1.44 + t2 = 0.21875 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = 0.21875 + 1.44 Combine like terms: 0.21875 + 1.44 = 1.65875 1.44 + -2.4t + t2 = 1.65875 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = 1.65875 Calculate the square root of the right side: 1.287924687 Break this problem into two subproblems by setting (t + -1.2) equal to 1.287924687 and -1.287924687.Subproblem 1
t + -1.2 = 1.287924687 Simplifying t + -1.2 = 1.287924687 Reorder the terms: -1.2 + t = 1.287924687 Solving -1.2 + t = 1.287924687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = 1.287924687 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 1.287924687 + 1.2 t = 1.287924687 + 1.2 Combine like terms: 1.287924687 + 1.2 = 2.487924687 t = 2.487924687 Simplifying t = 2.487924687Subproblem 2
t + -1.2 = -1.287924687 Simplifying t + -1.2 = -1.287924687 Reorder the terms: -1.2 + t = -1.287924687 Solving -1.2 + t = -1.287924687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = -1.287924687 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -1.287924687 + 1.2 t = -1.287924687 + 1.2 Combine like terms: -1.287924687 + 1.2 = -0.087924687 t = -0.087924687 Simplifying t = -0.087924687Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.487924687, -0.087924687}
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