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Simplifying 16t2 + -9.8t + -144 = 0 Reorder the terms: -144 + -9.8t + 16t2 = 0 Solving -144 + -9.8t + 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'. -9 + -0.6125t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.6125t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -0.6125t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.6125t + t2 = 0 + 9 -0.6125t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.6125t + t2 = 9 The t term is -0.6125t. Take half its coefficient (-0.30625). Square it (0.0937890625) and add it to both sides. Add '0.0937890625' to each side of the equation. -0.6125t + 0.0937890625 + t2 = 9 + 0.0937890625 Reorder the terms: 0.0937890625 + -0.6125t + t2 = 9 + 0.0937890625 Combine like terms: 9 + 0.0937890625 = 9.0937890625 0.0937890625 + -0.6125t + t2 = 9.0937890625 Factor a perfect square on the left side: (t + -0.30625)(t + -0.30625) = 9.0937890625 Calculate the square root of the right side: 3.015590997 Break this problem into two subproblems by setting (t + -0.30625) equal to 3.015590997 and -3.015590997.Subproblem 1
t + -0.30625 = 3.015590997 Simplifying t + -0.30625 = 3.015590997 Reorder the terms: -0.30625 + t = 3.015590997 Solving -0.30625 + t = 3.015590997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.30625' to each side of the equation. -0.30625 + 0.30625 + t = 3.015590997 + 0.30625 Combine like terms: -0.30625 + 0.30625 = 0.00000 0.00000 + t = 3.015590997 + 0.30625 t = 3.015590997 + 0.30625 Combine like terms: 3.015590997 + 0.30625 = 3.321840997 t = 3.321840997 Simplifying t = 3.321840997Subproblem 2
t + -0.30625 = -3.015590997 Simplifying t + -0.30625 = -3.015590997 Reorder the terms: -0.30625 + t = -3.015590997 Solving -0.30625 + t = -3.015590997 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.30625' to each side of the equation. -0.30625 + 0.30625 + t = -3.015590997 + 0.30625 Combine like terms: -0.30625 + 0.30625 = 0.00000 0.00000 + t = -3.015590997 + 0.30625 t = -3.015590997 + 0.30625 Combine like terms: -3.015590997 + 0.30625 = -2.709340997 t = -2.709340997 Simplifying t = -2.709340997Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.321840997, -2.709340997}
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