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Simplifying 16 = 16t2 + 30t + 4 Reorder the terms: 16 = 4 + 30t + 16t2 Solving 16 = 4 + 30t + 16t2 Solving for variable 't'. Combine like terms: 16 + -4 = 12 12 + -30t + -16t2 = 4 + 30t + 16t2 + -4 + -30t + -16t2 Reorder the terms: 12 + -30t + -16t2 = 4 + -4 + 30t + -30t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 12 + -30t + -16t2 = 0 + 30t + -30t + 16t2 + -16t2 12 + -30t + -16t2 = 30t + -30t + 16t2 + -16t2 Combine like terms: 30t + -30t = 0 12 + -30t + -16t2 = 0 + 16t2 + -16t2 12 + -30t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 12 + -30t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -15t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -15t + -8t2)' equal to zero and attempt to solve: Simplifying 6 + -15t + -8t2 = 0 Solving 6 + -15t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.75 + 1.875t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 1.875t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 1.875t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 1.875t + t2 = 0 + 0.75 1.875t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 1.875t + t2 = 0.75 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 = 0.75 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 0.75 + 0.87890625 Combine like terms: 0.75 + 0.87890625 = 1.62890625 0.87890625 + 1.875t + t2 = 1.62890625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 1.62890625 Calculate the square root of the right side: 1.276286116 Break this problem into two subproblems by setting (t + 0.9375) equal to 1.276286116 and -1.276286116.Subproblem 1
t + 0.9375 = 1.276286116 Simplifying t + 0.9375 = 1.276286116 Reorder the terms: 0.9375 + t = 1.276286116 Solving 0.9375 + t = 1.276286116 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 = 1.276286116 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 1.276286116 + -0.9375 t = 1.276286116 + -0.9375 Combine like terms: 1.276286116 + -0.9375 = 0.338786116 t = 0.338786116 Simplifying t = 0.338786116Subproblem 2
t + 0.9375 = -1.276286116 Simplifying t + 0.9375 = -1.276286116 Reorder the terms: 0.9375 + t = -1.276286116 Solving 0.9375 + t = -1.276286116 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 = -1.276286116 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -1.276286116 + -0.9375 t = -1.276286116 + -0.9375 Combine like terms: -1.276286116 + -0.9375 = -2.213786116 t = -2.213786116 Simplifying t = -2.213786116Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.338786116, -2.213786116}Solution
t = {0.338786116, -2.213786116}
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