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Simplifying -16t2 + 54t + 3 = 0 Reorder the terms: 3 + 54t + -16t2 = 0 Solving 3 + 54t + -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'. -0.1875 + -3.375t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -3.375t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -3.375t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -3.375t + t2 = 0 + 0.1875 -3.375t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -3.375t + t2 = 0.1875 The t term is -3.375t. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375t + 2.84765625 + t2 = 0.1875 + 2.84765625 Reorder the terms: 2.84765625 + -3.375t + t2 = 0.1875 + 2.84765625 Combine like terms: 0.1875 + 2.84765625 = 3.03515625 2.84765625 + -3.375t + t2 = 3.03515625 Factor a perfect square on the left side: (t + -1.6875)(t + -1.6875) = 3.03515625 Calculate the square root of the right side: 1.742169983 Break this problem into two subproblems by setting (t + -1.6875) equal to 1.742169983 and -1.742169983.Subproblem 1
t + -1.6875 = 1.742169983 Simplifying t + -1.6875 = 1.742169983 Reorder the terms: -1.6875 + t = 1.742169983 Solving -1.6875 + t = 1.742169983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + t = 1.742169983 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + t = 1.742169983 + 1.6875 t = 1.742169983 + 1.6875 Combine like terms: 1.742169983 + 1.6875 = 3.429669983 t = 3.429669983 Simplifying t = 3.429669983Subproblem 2
t + -1.6875 = -1.742169983 Simplifying t + -1.6875 = -1.742169983 Reorder the terms: -1.6875 + t = -1.742169983 Solving -1.6875 + t = -1.742169983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + t = -1.742169983 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + t = -1.742169983 + 1.6875 t = -1.742169983 + 1.6875 Combine like terms: -1.742169983 + 1.6875 = -0.054669983 t = -0.054669983 Simplifying t = -0.054669983Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.429669983, -0.054669983}
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