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Simplifying 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 = 3.765625 3.515625 + -3.75t + t2 = 3.765625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (t + -1.875) equal to 1.940521837 and -1.940521837.Subproblem 1
t + -1.875 = 1.940521837 Simplifying t + -1.875 = 1.940521837 Reorder the terms: -1.875 + t = 1.940521837 Solving -1.875 + t = 1.940521837 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 = 1.940521837 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 1.940521837 + 1.875 t = 1.940521837 + 1.875 Combine like terms: 1.940521837 + 1.875 = 3.815521837 t = 3.815521837 Simplifying t = 3.815521837Subproblem 2
t + -1.875 = -1.940521837 Simplifying t + -1.875 = -1.940521837 Reorder the terms: -1.875 + t = -1.940521837 Solving -1.875 + t = -1.940521837 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 = -1.940521837 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -1.940521837 + 1.875 t = -1.940521837 + 1.875 Combine like terms: -1.940521837 + 1.875 = -0.065521837 t = -0.065521837 Simplifying t = -0.065521837Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.815521837, -0.065521837}Solution
t = {3.815521837, -0.065521837}
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