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Simplifying 0 = -12t2 + 480t + 30 Reorder the terms: 0 = 30 + 480t + -12t2 Solving 0 = 30 + 480t + -12t2 Solving for variable 't'. Combine like terms: 0 + -30 = -30 -30 + -480t + 12t2 = 30 + 480t + -12t2 + -30 + -480t + 12t2 Reorder the terms: -30 + -480t + 12t2 = 30 + -30 + 480t + -480t + -12t2 + 12t2 Combine like terms: 30 + -30 = 0 -30 + -480t + 12t2 = 0 + 480t + -480t + -12t2 + 12t2 -30 + -480t + 12t2 = 480t + -480t + -12t2 + 12t2 Combine like terms: 480t + -480t = 0 -30 + -480t + 12t2 = 0 + -12t2 + 12t2 -30 + -480t + 12t2 = -12t2 + 12t2 Combine like terms: -12t2 + 12t2 = 0 -30 + -480t + 12t2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + -80t + 2t2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + -80t + 2t2)' equal to zero and attempt to solve: Simplifying -5 + -80t + 2t2 = 0 Solving -5 + -80t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -40t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -40t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -40t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -40t + t2 = 0 + 2.5 -40t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -40t + t2 = 2.5 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = 2.5 + 400 Reorder the terms: 400 + -40t + t2 = 2.5 + 400 Combine like terms: 2.5 + 400 = 402.5 400 + -40t + t2 = 402.5 Factor a perfect square on the left side: (t + -20)(t + -20) = 402.5 Calculate the square root of the right side: 20.062402648 Break this problem into two subproblems by setting (t + -20) equal to 20.062402648 and -20.062402648.Subproblem 1
t + -20 = 20.062402648 Simplifying t + -20 = 20.062402648 Reorder the terms: -20 + t = 20.062402648 Solving -20 + t = 20.062402648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 20.062402648 + 20 Combine like terms: -20 + 20 = 0 0 + t = 20.062402648 + 20 t = 20.062402648 + 20 Combine like terms: 20.062402648 + 20 = 40.062402648 t = 40.062402648 Simplifying t = 40.062402648Subproblem 2
t + -20 = -20.062402648 Simplifying t + -20 = -20.062402648 Reorder the terms: -20 + t = -20.062402648 Solving -20 + t = -20.062402648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -20.062402648 + 20 Combine like terms: -20 + 20 = 0 0 + t = -20.062402648 + 20 t = -20.062402648 + 20 Combine like terms: -20.062402648 + 20 = -0.062402648 t = -0.062402648 Simplifying t = -0.062402648Solution
The solution to the problem is based on the solutions from the subproblems. t = {40.062402648, -0.062402648}Solution
t = {40.062402648, -0.062402648}
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