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Simplifying 1.5 = -16t2 + 96t + 10 Reorder the terms: 1.5 = 10 + 96t + -16t2 Solving 1.5 = 10 + 96t + -16t2 Solving for variable 't'. Combine like terms: 1.5 + -10 = -8.5 -8.5 + -96t + 16t2 = 10 + 96t + -16t2 + -10 + -96t + 16t2 Reorder the terms: -8.5 + -96t + 16t2 = 10 + -10 + 96t + -96t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -8.5 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -8.5 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -8.5 + -96t + 16t2 = 0 + -16t2 + 16t2 -8.5 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -8.5 + -96t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.53125 + -6t + t2 = 0 Move the constant term to the right: Add '0.53125' to each side of the equation. -0.53125 + -6t + 0.53125 + t2 = 0 + 0.53125 Reorder the terms: -0.53125 + 0.53125 + -6t + t2 = 0 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + -6t + t2 = 0 + 0.53125 -6t + t2 = 0 + 0.53125 Combine like terms: 0 + 0.53125 = 0.53125 -6t + t2 = 0.53125 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 0.53125 + 9 Reorder the terms: 9 + -6t + t2 = 0.53125 + 9 Combine like terms: 0.53125 + 9 = 9.53125 9 + -6t + t2 = 9.53125 Factor a perfect square on the left side: (t + -3)(t + -3) = 9.53125 Calculate the square root of the right side: 3.087272259 Break this problem into two subproblems by setting (t + -3) equal to 3.087272259 and -3.087272259.Subproblem 1
t + -3 = 3.087272259 Simplifying t + -3 = 3.087272259 Reorder the terms: -3 + t = 3.087272259 Solving -3 + t = 3.087272259 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 3.087272259 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.087272259 + 3 t = 3.087272259 + 3 Combine like terms: 3.087272259 + 3 = 6.087272259 t = 6.087272259 Simplifying t = 6.087272259Subproblem 2
t + -3 = -3.087272259 Simplifying t + -3 = -3.087272259 Reorder the terms: -3 + t = -3.087272259 Solving -3 + t = -3.087272259 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -3.087272259 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.087272259 + 3 t = -3.087272259 + 3 Combine like terms: -3.087272259 + 3 = -0.087272259 t = -0.087272259 Simplifying t = -0.087272259Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.087272259, -0.087272259}
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