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Simplifying 16t2 + -96t + -4 = 144 Reorder the terms: -4 + -96t + 16t2 = 144 Solving -4 + -96t + 16t2 = 144 Solving for variable 't'. Reorder the terms: -4 + -144 + -96t + 16t2 = 144 + -144 Combine like terms: -4 + -144 = -148 -148 + -96t + 16t2 = 144 + -144 Combine like terms: 144 + -144 = 0 -148 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-37 + -24t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-37 + -24t + 4t2)' equal to zero and attempt to solve: Simplifying -37 + -24t + 4t2 = 0 Solving -37 + -24t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + -6t + t2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + -6t + 9.25 + t2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + -6t + t2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + -6t + t2 = 0 + 9.25 -6t + t2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 -6t + t2 = 9.25 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 = 9.25 + 9 Reorder the terms: 9 + -6t + t2 = 9.25 + 9 Combine like terms: 9.25 + 9 = 18.25 9 + -6t + t2 = 18.25 Factor a perfect square on the left side: (t + -3)(t + -3) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (t + -3) equal to 4.272001873 and -4.272001873.Subproblem 1
t + -3 = 4.272001873 Simplifying t + -3 = 4.272001873 Reorder the terms: -3 + t = 4.272001873 Solving -3 + t = 4.272001873 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 = 4.272001873 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.272001873 + 3 t = 4.272001873 + 3 Combine like terms: 4.272001873 + 3 = 7.272001873 t = 7.272001873 Simplifying t = 7.272001873Subproblem 2
t + -3 = -4.272001873 Simplifying t + -3 = -4.272001873 Reorder the terms: -3 + t = -4.272001873 Solving -3 + t = -4.272001873 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 = -4.272001873 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.272001873 + 3 t = -4.272001873 + 3 Combine like terms: -4.272001873 + 3 = -1.272001873 t = -1.272001873 Simplifying t = -1.272001873Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.272001873, -1.272001873}Solution
t = {7.272001873, -1.272001873}
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