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Simplifying 0 = 16t2 + 60t + 4 Reorder the terms: 0 = 4 + 60t + 16t2 Solving 0 = 4 + 60t + 16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -60t + -16t2 = 4 + 60t + 16t2 + -4 + -60t + -16t2 Reorder the terms: -4 + -60t + -16t2 = 4 + -4 + 60t + -60t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -60t + -16t2 = 0 + 60t + -60t + 16t2 + -16t2 -4 + -60t + -16t2 = 60t + -60t + 16t2 + -16t2 Combine like terms: 60t + -60t = 0 -4 + -60t + -16t2 = 0 + 16t2 + -16t2 -4 + -60t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -60t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(1 + 15t + 4t2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(1 + 15t + 4t2)' equal to zero and attempt to solve: Simplifying 1 + 15t + 4t2 = 0 Solving 1 + 15t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 3.75t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.75t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.75t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.75t + t2 = 0 + -0.25 3.75t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.75t + t2 = -0.25 The t term is 3.75t. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75t + 3.515625 + t2 = -0.25 + 3.515625 Reorder the terms: 3.515625 + 3.75t + t2 = -0.25 + 3.515625 Combine like terms: -0.25 + 3.515625 = 3.265625 3.515625 + 3.75t + t2 = 3.265625 Factor a perfect square on the left side: (t + 1.875)(t + 1.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (t + 1.875) equal to 1.807104037 and -1.807104037.Subproblem 1
t + 1.875 = 1.807104037 Simplifying t + 1.875 = 1.807104037 Reorder the terms: 1.875 + t = 1.807104037 Solving 1.875 + t = 1.807104037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = 1.807104037 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = 1.807104037 + -1.875 t = 1.807104037 + -1.875 Combine like terms: 1.807104037 + -1.875 = -0.067895963 t = -0.067895963 Simplifying t = -0.067895963Subproblem 2
t + 1.875 = -1.807104037 Simplifying t + 1.875 = -1.807104037 Reorder the terms: 1.875 + t = -1.807104037 Solving 1.875 + t = -1.807104037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + t = -1.807104037 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + t = -1.807104037 + -1.875 t = -1.807104037 + -1.875 Combine like terms: -1.807104037 + -1.875 = -3.682104037 t = -3.682104037 Simplifying t = -3.682104037Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.067895963, -3.682104037}Solution
t = {-0.067895963, -3.682104037}
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