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Simplifying 33 = -16t2 + 80t + 5 Reorder the terms: 33 = 5 + 80t + -16t2 Solving 33 = 5 + 80t + -16t2 Solving for variable 't'. Combine like terms: 33 + -5 = 28 28 + -80t + 16t2 = 5 + 80t + -16t2 + -5 + -80t + 16t2 Reorder the terms: 28 + -80t + 16t2 = 5 + -5 + 80t + -80t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 28 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2 28 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2 Combine like terms: 80t + -80t = 0 28 + -80t + 16t2 = 0 + -16t2 + 16t2 28 + -80t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 28 + -80t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -20t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -20t + 4t2)' equal to zero and attempt to solve: Simplifying 7 + -20t + 4t2 = 0 Solving 7 + -20t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -5t + t2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -5t + -1.75 + t2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -5t + t2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -5t + t2 = 0 + -1.75 -5t + t2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -5t + t2 = -1.75 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -1.75 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -1.75 + 6.25 Combine like terms: -1.75 + 6.25 = 4.5 6.25 + -5t + t2 = 4.5 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (t + -2.5) equal to 2.121320344 and -2.121320344.Subproblem 1
t + -2.5 = 2.121320344 Simplifying t + -2.5 = 2.121320344 Reorder the terms: -2.5 + t = 2.121320344 Solving -2.5 + t = 2.121320344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.121320344 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.121320344 + 2.5 t = 2.121320344 + 2.5 Combine like terms: 2.121320344 + 2.5 = 4.621320344 t = 4.621320344 Simplifying t = 4.621320344Subproblem 2
t + -2.5 = -2.121320344 Simplifying t + -2.5 = -2.121320344 Reorder the terms: -2.5 + t = -2.121320344 Solving -2.5 + t = -2.121320344 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.121320344 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.121320344 + 2.5 t = -2.121320344 + 2.5 Combine like terms: -2.121320344 + 2.5 = 0.378679656 t = 0.378679656 Simplifying t = 0.378679656Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.621320344, 0.378679656}Solution
t = {4.621320344, 0.378679656}
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