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Simplifying 0 = -16t2 + 96t + 72 Reorder the terms: 0 = 72 + 96t + -16t2 Solving 0 = 72 + 96t + -16t2 Solving for variable 't'. Combine like terms: 0 + -72 = -72 -72 + -96t + 16t2 = 72 + 96t + -16t2 + -72 + -96t + 16t2 Reorder the terms: -72 + -96t + 16t2 = 72 + -72 + 96t + -96t + -16t2 + 16t2 Combine like terms: 72 + -72 = 0 -72 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -72 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -72 + -96t + 16t2 = 0 + -16t2 + 16t2 -72 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -72 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-9 + -12t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-9 + -12t + 2t2)' equal to zero and attempt to solve: Simplifying -9 + -12t + 2t2 = 0 Solving -9 + -12t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -6t + t2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -6t + 4.5 + t2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -6t + t2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -6t + t2 = 0 + 4.5 -6t + t2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -6t + t2 = 4.5 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 = 4.5 + 9 Reorder the terms: 9 + -6t + t2 = 4.5 + 9 Combine like terms: 4.5 + 9 = 13.5 9 + -6t + t2 = 13.5 Factor a perfect square on the left side: (t + -3)(t + -3) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (t + -3) equal to 3.674234614 and -3.674234614.Subproblem 1
t + -3 = 3.674234614 Simplifying t + -3 = 3.674234614 Reorder the terms: -3 + t = 3.674234614 Solving -3 + t = 3.674234614 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 = 3.674234614 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.674234614 + 3 t = 3.674234614 + 3 Combine like terms: 3.674234614 + 3 = 6.674234614 t = 6.674234614 Simplifying t = 6.674234614Subproblem 2
t + -3 = -3.674234614 Simplifying t + -3 = -3.674234614 Reorder the terms: -3 + t = -3.674234614 Solving -3 + t = -3.674234614 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 = -3.674234614 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.674234614 + 3 t = -3.674234614 + 3 Combine like terms: -3.674234614 + 3 = -0.674234614 t = -0.674234614 Simplifying t = -0.674234614Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.674234614, -0.674234614}Solution
t = {6.674234614, -0.674234614}
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