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Simplifying 24 + 320t + -16t2 = 0 Solving 24 + 320t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(3 + 40t + -2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(3 + 40t + -2t2)' equal to zero and attempt to solve: Simplifying 3 + 40t + -2t2 = 0 Solving 3 + 40t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + -20t + t2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -20t + 1.5 + t2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -20t + t2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -20t + t2 = 0 + 1.5 -20t + t2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -20t + t2 = 1.5 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 1.5 + 100 Reorder the terms: 100 + -20t + t2 = 1.5 + 100 Combine like terms: 1.5 + 100 = 101.5 100 + -20t + t2 = 101.5 Factor a perfect square on the left side: (t + -10)(t + -10) = 101.5 Calculate the square root of the right side: 10.07472084 Break this problem into two subproblems by setting (t + -10) equal to 10.07472084 and -10.07472084.Subproblem 1
t + -10 = 10.07472084 Simplifying t + -10 = 10.07472084 Reorder the terms: -10 + t = 10.07472084 Solving -10 + t = 10.07472084 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 10.07472084 + 10 Combine like terms: -10 + 10 = 0 0 + t = 10.07472084 + 10 t = 10.07472084 + 10 Combine like terms: 10.07472084 + 10 = 20.07472084 t = 20.07472084 Simplifying t = 20.07472084Subproblem 2
t + -10 = -10.07472084 Simplifying t + -10 = -10.07472084 Reorder the terms: -10 + t = -10.07472084 Solving -10 + t = -10.07472084 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -10.07472084 + 10 Combine like terms: -10 + 10 = 0 0 + t = -10.07472084 + 10 t = -10.07472084 + 10 Combine like terms: -10.07472084 + 10 = -0.07472084 t = -0.07472084 Simplifying t = -0.07472084Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.07472084, -0.07472084}Solution
t = {20.07472084, -0.07472084}
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