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Simplifying 0 = -16t2 + 120t + 2 Reorder the terms: 0 = 2 + 120t + -16t2 Solving 0 = 2 + 120t + -16t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -120t + 16t2 = 2 + 120t + -16t2 + -2 + -120t + 16t2 Reorder the terms: -2 + -120t + 16t2 = 2 + -2 + 120t + -120t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 -2 + -120t + 16t2 = 0 + 120t + -120t + -16t2 + 16t2 -2 + -120t + 16t2 = 120t + -120t + -16t2 + 16t2 Combine like terms: 120t + -120t = 0 -2 + -120t + 16t2 = 0 + -16t2 + 16t2 -2 + -120t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -2 + -120t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -60t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -60t + 8t2)' equal to zero and attempt to solve: Simplifying -1 + -60t + 8t2 = 0 Solving -1 + -60t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -7.5t + t2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -7.5t + 0.125 + t2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -7.5t + t2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -7.5t + t2 = 0 + 0.125 -7.5t + t2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -7.5t + t2 = 0.125 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = 0.125 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = 0.125 + 14.0625 Combine like terms: 0.125 + 14.0625 = 14.1875 14.0625 + -7.5t + t2 = 14.1875 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 14.1875 Calculate the square root of the right side: 3.766629793 Break this problem into two subproblems by setting (t + -3.75) equal to 3.766629793 and -3.766629793.Subproblem 1
t + -3.75 = 3.766629793 Simplifying t + -3.75 = 3.766629793 Reorder the terms: -3.75 + t = 3.766629793 Solving -3.75 + t = 3.766629793 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 3.766629793 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 3.766629793 + 3.75 t = 3.766629793 + 3.75 Combine like terms: 3.766629793 + 3.75 = 7.516629793 t = 7.516629793 Simplifying t = 7.516629793Subproblem 2
t + -3.75 = -3.766629793 Simplifying t + -3.75 = -3.766629793 Reorder the terms: -3.75 + t = -3.766629793 Solving -3.75 + t = -3.766629793 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -3.766629793 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -3.766629793 + 3.75 t = -3.766629793 + 3.75 Combine like terms: -3.766629793 + 3.75 = -0.016629793 t = -0.016629793 Simplifying t = -0.016629793Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.516629793, -0.016629793}Solution
t = {7.516629793, -0.016629793}
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