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Simplifying 0 = 16t2 + 96t + -140 Reorder the terms: 0 = -140 + 96t + 16t2 Solving 0 = -140 + 96t + 16t2 Solving for variable 't'. Combine like terms: 0 + 140 = 140 140 + -96t + -16t2 = -140 + 96t + 16t2 + 140 + -96t + -16t2 Reorder the terms: 140 + -96t + -16t2 = -140 + 140 + 96t + -96t + 16t2 + -16t2 Combine like terms: -140 + 140 = 0 140 + -96t + -16t2 = 0 + 96t + -96t + 16t2 + -16t2 140 + -96t + -16t2 = 96t + -96t + 16t2 + -16t2 Combine like terms: 96t + -96t = 0 140 + -96t + -16t2 = 0 + 16t2 + -16t2 140 + -96t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 140 + -96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -24t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + -24t + -4t2)' equal to zero and attempt to solve: Simplifying 35 + -24t + -4t2 = 0 Solving 35 + -24t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -8.75 + 6t + t2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 6t + 8.75 + t2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 6t + t2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 6t + t2 = 0 + 8.75 6t + t2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 6t + t2 = 8.75 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 = 8.75 + 9 Reorder the terms: 9 + 6t + t2 = 8.75 + 9 Combine like terms: 8.75 + 9 = 17.75 9 + 6t + t2 = 17.75 Factor a perfect square on the left side: (t + 3)(t + 3) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (t + 3) equal to 4.213074887 and -4.213074887.Subproblem 1
t + 3 = 4.213074887 Simplifying t + 3 = 4.213074887 Reorder the terms: 3 + t = 4.213074887 Solving 3 + t = 4.213074887 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 = 4.213074887 + -3 Combine like terms: 3 + -3 = 0 0 + t = 4.213074887 + -3 t = 4.213074887 + -3 Combine like terms: 4.213074887 + -3 = 1.213074887 t = 1.213074887 Simplifying t = 1.213074887Subproblem 2
t + 3 = -4.213074887 Simplifying t + 3 = -4.213074887 Reorder the terms: 3 + t = -4.213074887 Solving 3 + t = -4.213074887 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 = -4.213074887 + -3 Combine like terms: 3 + -3 = 0 0 + t = -4.213074887 + -3 t = -4.213074887 + -3 Combine like terms: -4.213074887 + -3 = -7.213074887 t = -7.213074887 Simplifying t = -7.213074887Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.213074887, -7.213074887}Solution
t = {1.213074887, -7.213074887}
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