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Simplifying -16t2 + 128t = 213 Reorder the terms: 128t + -16t2 = 213 Solving 128t + -16t2 = 213 Solving for variable 't'. Reorder the terms: -213 + 128t + -16t2 = 213 + -213 Combine like terms: 213 + -213 = 0 -213 + 128t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 13.3125 + -8t + t2 = 0 Move the constant term to the right: Add '-13.3125' to each side of the equation. 13.3125 + -8t + -13.3125 + t2 = 0 + -13.3125 Reorder the terms: 13.3125 + -13.3125 + -8t + t2 = 0 + -13.3125 Combine like terms: 13.3125 + -13.3125 = 0.0000 0.0000 + -8t + t2 = 0 + -13.3125 -8t + t2 = 0 + -13.3125 Combine like terms: 0 + -13.3125 = -13.3125 -8t + t2 = -13.3125 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -13.3125 + 16 Reorder the terms: 16 + -8t + t2 = -13.3125 + 16 Combine like terms: -13.3125 + 16 = 2.6875 16 + -8t + t2 = 2.6875 Factor a perfect square on the left side: (t + -4)(t + -4) = 2.6875 Calculate the square root of the right side: 1.639359631 Break this problem into two subproblems by setting (t + -4) equal to 1.639359631 and -1.639359631.Subproblem 1
t + -4 = 1.639359631 Simplifying t + -4 = 1.639359631 Reorder the terms: -4 + t = 1.639359631 Solving -4 + t = 1.639359631 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 1.639359631 + 4 Combine like terms: -4 + 4 = 0 0 + t = 1.639359631 + 4 t = 1.639359631 + 4 Combine like terms: 1.639359631 + 4 = 5.639359631 t = 5.639359631 Simplifying t = 5.639359631Subproblem 2
t + -4 = -1.639359631 Simplifying t + -4 = -1.639359631 Reorder the terms: -4 + t = -1.639359631 Solving -4 + t = -1.639359631 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -1.639359631 + 4 Combine like terms: -4 + 4 = 0 0 + t = -1.639359631 + 4 t = -1.639359631 + 4 Combine like terms: -1.639359631 + 4 = 2.360640369 t = 2.360640369 Simplifying t = 2.360640369Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.639359631, 2.360640369}
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