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Simplifying 128 = 16t2 + -96t Reorder the terms: 128 = -96t + 16t2 Solving 128 = -96t + 16t2 Solving for variable 't'. Reorder the terms: 128 + 96t + -16t2 = -96t + 96t + 16t2 + -16t2 Combine like terms: -96t + 96t = 0 128 + 96t + -16t2 = 0 + 16t2 + -16t2 128 + 96t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 128 + 96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(8 + 6t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(8 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying 8 + 6t + -1t2 = 0 Solving 8 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -6t + t2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -6t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + -6t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6t + t2 = 0 + 8 -6t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6t + t2 = 8 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 = 8 + 9 Reorder the terms: 9 + -6t + t2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6t + t2 = 17 Factor a perfect square on the left side: (t + -3)(t + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (t + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
t + -3 = 4.123105626 Simplifying t + -3 = 4.123105626 Reorder the terms: -3 + t = 4.123105626 Solving -3 + t = 4.123105626 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 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.123105626 + 3 t = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 t = 7.123105626 Simplifying t = 7.123105626Subproblem 2
t + -3 = -4.123105626 Simplifying t + -3 = -4.123105626 Reorder the terms: -3 + t = -4.123105626 Solving -3 + t = -4.123105626 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 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.123105626 + 3 t = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 t = -1.123105626 Simplifying t = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.123105626, -1.123105626}Solution
t = {7.123105626, -1.123105626}
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