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Simplifying 16t2 + 30t + 4 = 0 Reorder the terms: 4 + 30t + 16t2 = 0 Solving 4 + 30t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 15t + 8t2)' equal to zero and attempt to solve: Simplifying 2 + 15t + 8t2 = 0 Solving 2 + 15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + 1.875t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.875t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.875t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.875t + t2 = 0 + -0.25 1.875t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.875t + t2 = -0.25 The t term is 1.875t. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875t + 0.87890625 + t2 = -0.25 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = -0.25 + 0.87890625 Combine like terms: -0.25 + 0.87890625 = 0.62890625 0.87890625 + 1.875t + t2 = 0.62890625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (t + 0.9375) equal to 0.793036096 and -0.793036096.Subproblem 1
t + 0.9375 = 0.793036096 Simplifying t + 0.9375 = 0.793036096 Reorder the terms: 0.9375 + t = 0.793036096 Solving 0.9375 + t = 0.793036096 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = 0.793036096 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 0.793036096 + -0.9375 t = 0.793036096 + -0.9375 Combine like terms: 0.793036096 + -0.9375 = -0.144463904 t = -0.144463904 Simplifying t = -0.144463904Subproblem 2
t + 0.9375 = -0.793036096 Simplifying t + 0.9375 = -0.793036096 Reorder the terms: 0.9375 + t = -0.793036096 Solving 0.9375 + t = -0.793036096 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = -0.793036096 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -0.793036096 + -0.9375 t = -0.793036096 + -0.9375 Combine like terms: -0.793036096 + -0.9375 = -1.730536096 t = -1.730536096 Simplifying t = -1.730536096Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.144463904, -1.730536096}Solution
t = {-0.144463904, -1.730536096}
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