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Simplifying 25 + -3 = 16t2 + 96t Combine like terms: 25 + -3 = 22 22 = 16t2 + 96t Reorder the terms: 22 = 96t + 16t2 Solving 22 = 96t + 16t2 Solving for variable 't'. Reorder the terms: 22 + -96t + -16t2 = 96t + -96t + 16t2 + -16t2 Combine like terms: 96t + -96t = 0 22 + -96t + -16t2 = 0 + 16t2 + -16t2 22 + -96t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 22 + -96t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -48t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -48t + -8t2)' equal to zero and attempt to solve: Simplifying 11 + -48t + -8t2 = 0 Solving 11 + -48t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.375 + 6t + t2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 6t + 1.375 + t2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 6t + t2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 6t + t2 = 0 + 1.375 6t + t2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 6t + t2 = 1.375 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 = 1.375 + 9 Reorder the terms: 9 + 6t + t2 = 1.375 + 9 Combine like terms: 1.375 + 9 = 10.375 9 + 6t + t2 = 10.375 Factor a perfect square on the left side: (t + 3)(t + 3) = 10.375 Calculate the square root of the right side: 3.221024682 Break this problem into two subproblems by setting (t + 3) equal to 3.221024682 and -3.221024682.Subproblem 1
t + 3 = 3.221024682 Simplifying t + 3 = 3.221024682 Reorder the terms: 3 + t = 3.221024682 Solving 3 + t = 3.221024682 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 = 3.221024682 + -3 Combine like terms: 3 + -3 = 0 0 + t = 3.221024682 + -3 t = 3.221024682 + -3 Combine like terms: 3.221024682 + -3 = 0.221024682 t = 0.221024682 Simplifying t = 0.221024682Subproblem 2
t + 3 = -3.221024682 Simplifying t + 3 = -3.221024682 Reorder the terms: 3 + t = -3.221024682 Solving 3 + t = -3.221024682 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 = -3.221024682 + -3 Combine like terms: 3 + -3 = 0 0 + t = -3.221024682 + -3 t = -3.221024682 + -3 Combine like terms: -3.221024682 + -3 = -6.221024682 t = -6.221024682 Simplifying t = -6.221024682Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.221024682, -6.221024682}Solution
t = {0.221024682, -6.221024682}
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