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Simplifying 3t2 + -48t = 16 Reorder the terms: -48t + 3t2 = 16 Solving -48t + 3t2 = 16 Solving for variable 't'. Reorder the terms: -16 + -48t + 3t2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -48t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -16t + t2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -16t + 5.333333333 + t2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -16t + t2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -16t + t2 = 0 + 5.333333333 -16t + t2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -16t + t2 = 5.333333333 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = 5.333333333 + 64 Reorder the terms: 64 + -16t + t2 = 5.333333333 + 64 Combine like terms: 5.333333333 + 64 = 69.333333333 64 + -16t + t2 = 69.333333333 Factor a perfect square on the left side: (t + -8)(t + -8) = 69.333333333 Calculate the square root of the right side: 8.326663998 Break this problem into two subproblems by setting (t + -8) equal to 8.326663998 and -8.326663998.Subproblem 1
t + -8 = 8.326663998 Simplifying t + -8 = 8.326663998 Reorder the terms: -8 + t = 8.326663998 Solving -8 + t = 8.326663998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 8.326663998 + 8 Combine like terms: -8 + 8 = 0 0 + t = 8.326663998 + 8 t = 8.326663998 + 8 Combine like terms: 8.326663998 + 8 = 16.326663998 t = 16.326663998 Simplifying t = 16.326663998Subproblem 2
t + -8 = -8.326663998 Simplifying t + -8 = -8.326663998 Reorder the terms: -8 + t = -8.326663998 Solving -8 + t = -8.326663998 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -8.326663998 + 8 Combine like terms: -8 + 8 = 0 0 + t = -8.326663998 + 8 t = -8.326663998 + 8 Combine like terms: -8.326663998 + 8 = -0.326663998 t = -0.326663998 Simplifying t = -0.326663998Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.326663998, -0.326663998}
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