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Simplifying 450 = 4t2 + 18t Reorder the terms: 450 = 18t + 4t2 Solving 450 = 18t + 4t2 Solving for variable 't'. Reorder the terms: 450 + -18t + -4t2 = 18t + -18t + 4t2 + -4t2 Combine like terms: 18t + -18t = 0 450 + -18t + -4t2 = 0 + 4t2 + -4t2 450 + -18t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 450 + -18t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(225 + -9t + -2t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(225 + -9t + -2t2)' equal to zero and attempt to solve: Simplifying 225 + -9t + -2t2 = 0 Solving 225 + -9t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -112.5 + 4.5t + t2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + 4.5t + 112.5 + t2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + 4.5t + t2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + 4.5t + t2 = 0 + 112.5 4.5t + t2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 4.5t + t2 = 112.5 The t term is 4.5t. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5t + 5.0625 + t2 = 112.5 + 5.0625 Reorder the terms: 5.0625 + 4.5t + t2 = 112.5 + 5.0625 Combine like terms: 112.5 + 5.0625 = 117.5625 5.0625 + 4.5t + t2 = 117.5625 Factor a perfect square on the left side: (t + 2.25)(t + 2.25) = 117.5625 Calculate the square root of the right side: 10.842624221 Break this problem into two subproblems by setting (t + 2.25) equal to 10.842624221 and -10.842624221.Subproblem 1
t + 2.25 = 10.842624221 Simplifying t + 2.25 = 10.842624221 Reorder the terms: 2.25 + t = 10.842624221 Solving 2.25 + t = 10.842624221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + t = 10.842624221 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + t = 10.842624221 + -2.25 t = 10.842624221 + -2.25 Combine like terms: 10.842624221 + -2.25 = 8.592624221 t = 8.592624221 Simplifying t = 8.592624221Subproblem 2
t + 2.25 = -10.842624221 Simplifying t + 2.25 = -10.842624221 Reorder the terms: 2.25 + t = -10.842624221 Solving 2.25 + t = -10.842624221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + t = -10.842624221 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + t = -10.842624221 + -2.25 t = -10.842624221 + -2.25 Combine like terms: -10.842624221 + -2.25 = -13.092624221 t = -13.092624221 Simplifying t = -13.092624221Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.592624221, -13.092624221}Solution
t = {8.592624221, -13.092624221}
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