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Simplifying -16t2 + 150t + 25 = 0 Reorder the terms: 25 + 150t + -16t2 = 0 Solving 25 + 150t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.5625 + -9.375t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -9.375t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -9.375t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -9.375t + t2 = 0 + 1.5625 -9.375t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -9.375t + t2 = 1.5625 The t term is -9.375t. Take half its coefficient (-4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. -9.375t + 21.97265625 + t2 = 1.5625 + 21.97265625 Reorder the terms: 21.97265625 + -9.375t + t2 = 1.5625 + 21.97265625 Combine like terms: 1.5625 + 21.97265625 = 23.53515625 21.97265625 + -9.375t + t2 = 23.53515625 Factor a perfect square on the left side: (t + -4.6875)(t + -4.6875) = 23.53515625 Calculate the square root of the right side: 4.851304593 Break this problem into two subproblems by setting (t + -4.6875) equal to 4.851304593 and -4.851304593.Subproblem 1
t + -4.6875 = 4.851304593 Simplifying t + -4.6875 = 4.851304593 Reorder the terms: -4.6875 + t = 4.851304593 Solving -4.6875 + t = 4.851304593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = 4.851304593 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = 4.851304593 + 4.6875 t = 4.851304593 + 4.6875 Combine like terms: 4.851304593 + 4.6875 = 9.538804593 t = 9.538804593 Simplifying t = 9.538804593Subproblem 2
t + -4.6875 = -4.851304593 Simplifying t + -4.6875 = -4.851304593 Reorder the terms: -4.6875 + t = -4.851304593 Solving -4.6875 + t = -4.851304593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.6875' to each side of the equation. -4.6875 + 4.6875 + t = -4.851304593 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + t = -4.851304593 + 4.6875 t = -4.851304593 + 4.6875 Combine like terms: -4.851304593 + 4.6875 = -0.163804593 t = -0.163804593 Simplifying t = -0.163804593Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.538804593, -0.163804593}
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