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Simplifying 0 = -16t2 + 600t + 14400 Reorder the terms: 0 = 14400 + 600t + -16t2 Solving 0 = 14400 + 600t + -16t2 Solving for variable 't'. Combine like terms: 0 + -14400 = -14400 -14400 + -600t + 16t2 = 14400 + 600t + -16t2 + -14400 + -600t + 16t2 Reorder the terms: -14400 + -600t + 16t2 = 14400 + -14400 + 600t + -600t + -16t2 + 16t2 Combine like terms: 14400 + -14400 = 0 -14400 + -600t + 16t2 = 0 + 600t + -600t + -16t2 + 16t2 -14400 + -600t + 16t2 = 600t + -600t + -16t2 + 16t2 Combine like terms: 600t + -600t = 0 -14400 + -600t + 16t2 = 0 + -16t2 + 16t2 -14400 + -600t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -14400 + -600t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-1800 + -75t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1800 + -75t + 2t2)' equal to zero and attempt to solve: Simplifying -1800 + -75t + 2t2 = 0 Solving -1800 + -75t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -900 + -37.5t + t2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + -37.5t + 900 + t2 = 0 + 900 Reorder the terms: -900 + 900 + -37.5t + t2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + -37.5t + t2 = 0 + 900 -37.5t + t2 = 0 + 900 Combine like terms: 0 + 900 = 900 -37.5t + t2 = 900 The t term is -37.5t. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5t + 351.5625 + t2 = 900 + 351.5625 Reorder the terms: 351.5625 + -37.5t + t2 = 900 + 351.5625 Combine like terms: 900 + 351.5625 = 1251.5625 351.5625 + -37.5t + t2 = 1251.5625 Factor a perfect square on the left side: (t + -18.75)(t + -18.75) = 1251.5625 Calculate the square root of the right side: 35.377429245 Break this problem into two subproblems by setting (t + -18.75) equal to 35.377429245 and -35.377429245.Subproblem 1
t + -18.75 = 35.377429245 Simplifying t + -18.75 = 35.377429245 Reorder the terms: -18.75 + t = 35.377429245 Solving -18.75 + t = 35.377429245 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + t = 35.377429245 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + t = 35.377429245 + 18.75 t = 35.377429245 + 18.75 Combine like terms: 35.377429245 + 18.75 = 54.127429245 t = 54.127429245 Simplifying t = 54.127429245Subproblem 2
t + -18.75 = -35.377429245 Simplifying t + -18.75 = -35.377429245 Reorder the terms: -18.75 + t = -35.377429245 Solving -18.75 + t = -35.377429245 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + t = -35.377429245 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + t = -35.377429245 + 18.75 t = -35.377429245 + 18.75 Combine like terms: -35.377429245 + 18.75 = -16.627429245 t = -16.627429245 Simplifying t = -16.627429245Solution
The solution to the problem is based on the solutions from the subproblems. t = {54.127429245, -16.627429245}Solution
t = {54.127429245, -16.627429245}
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