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Simplifying 16t2 + 150t + 5 = 0 Reorder the terms: 5 + 150t + 16t2 = 0 Solving 5 + 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'. 0.3125 + 9.375t + t2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + 9.375t + -0.3125 + t2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + 9.375t + t2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + 9.375t + t2 = 0 + -0.3125 9.375t + t2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 9.375t + t2 = -0.3125 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 = -0.3125 + 21.97265625 Reorder the terms: 21.97265625 + 9.375t + t2 = -0.3125 + 21.97265625 Combine like terms: -0.3125 + 21.97265625 = 21.66015625 21.97265625 + 9.375t + t2 = 21.66015625 Factor a perfect square on the left side: (t + 4.6875)(t + 4.6875) = 21.66015625 Calculate the square root of the right side: 4.654047298 Break this problem into two subproblems by setting (t + 4.6875) equal to 4.654047298 and -4.654047298.Subproblem 1
t + 4.6875 = 4.654047298 Simplifying t + 4.6875 = 4.654047298 Reorder the terms: 4.6875 + t = 4.654047298 Solving 4.6875 + t = 4.654047298 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 = 4.654047298 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = 4.654047298 + -4.6875 t = 4.654047298 + -4.6875 Combine like terms: 4.654047298 + -4.6875 = -0.033452702 t = -0.033452702 Simplifying t = -0.033452702Subproblem 2
t + 4.6875 = -4.654047298 Simplifying t + 4.6875 = -4.654047298 Reorder the terms: 4.6875 + t = -4.654047298 Solving 4.6875 + t = -4.654047298 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 = -4.654047298 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + t = -4.654047298 + -4.6875 t = -4.654047298 + -4.6875 Combine like terms: -4.654047298 + -4.6875 = -9.341547298 t = -9.341547298 Simplifying t = -9.341547298Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.033452702, -9.341547298}
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