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Simplifying -16t2 + 38.4t + 0.96 = 0 Reorder the terms: 0.96 + 38.4t + -16t2 = 0 Solving 0.96 + 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'. -0.06 + -2.4t + t2 = 0 Move the constant term to the right: Add '0.06' to each side of the equation. -0.06 + -2.4t + 0.06 + t2 = 0 + 0.06 Reorder the terms: -0.06 + 0.06 + -2.4t + t2 = 0 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.00 + -2.4t + t2 = 0 + 0.06 -2.4t + t2 = 0 + 0.06 Combine like terms: 0 + 0.06 = 0.06 -2.4t + t2 = 0.06 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 = 0.06 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = 0.06 + 1.44 Combine like terms: 0.06 + 1.44 = 1.5 1.44 + -2.4t + t2 = 1.5 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (t + -1.2) equal to 1.224744871 and -1.224744871.Subproblem 1
t + -1.2 = 1.224744871 Simplifying t + -1.2 = 1.224744871 Reorder the terms: -1.2 + t = 1.224744871 Solving -1.2 + t = 1.224744871 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 = 1.224744871 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 1.224744871 + 1.2 t = 1.224744871 + 1.2 Combine like terms: 1.224744871 + 1.2 = 2.424744871 t = 2.424744871 Simplifying t = 2.424744871Subproblem 2
t + -1.2 = -1.224744871 Simplifying t + -1.2 = -1.224744871 Reorder the terms: -1.2 + t = -1.224744871 Solving -1.2 + t = -1.224744871 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 = -1.224744871 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -1.224744871 + 1.2 t = -1.224744871 + 1.2 Combine like terms: -1.224744871 + 1.2 = -0.024744871 t = -0.024744871 Simplifying t = -0.024744871Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.424744871, -0.024744871}
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