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Simplifying 29 = 33t + -5t2 Solving 29 = 33t + -5t2 Solving for variable 't'. Reorder the terms: 29 + -33t + 5t2 = 33t + -33t + -5t2 + 5t2 Combine like terms: 33t + -33t = 0 29 + -33t + 5t2 = 0 + -5t2 + 5t2 29 + -33t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 29 + -33t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.8 + -6.6t + t2 = 0 Move the constant term to the right: Add '-5.8' to each side of the equation. 5.8 + -6.6t + -5.8 + t2 = 0 + -5.8 Reorder the terms: 5.8 + -5.8 + -6.6t + t2 = 0 + -5.8 Combine like terms: 5.8 + -5.8 = 0.0 0.0 + -6.6t + t2 = 0 + -5.8 -6.6t + t2 = 0 + -5.8 Combine like terms: 0 + -5.8 = -5.8 -6.6t + t2 = -5.8 The t term is -6.6t. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6t + 10.89 + t2 = -5.8 + 10.89 Reorder the terms: 10.89 + -6.6t + t2 = -5.8 + 10.89 Combine like terms: -5.8 + 10.89 = 5.09 10.89 + -6.6t + t2 = 5.09 Factor a perfect square on the left side: (t + -3.3)(t + -3.3) = 5.09 Calculate the square root of the right side: 2.256102835 Break this problem into two subproblems by setting (t + -3.3) equal to 2.256102835 and -2.256102835.Subproblem 1
t + -3.3 = 2.256102835 Simplifying t + -3.3 = 2.256102835 Reorder the terms: -3.3 + t = 2.256102835 Solving -3.3 + t = 2.256102835 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + t = 2.256102835 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + t = 2.256102835 + 3.3 t = 2.256102835 + 3.3 Combine like terms: 2.256102835 + 3.3 = 5.556102835 t = 5.556102835 Simplifying t = 5.556102835Subproblem 2
t + -3.3 = -2.256102835 Simplifying t + -3.3 = -2.256102835 Reorder the terms: -3.3 + t = -2.256102835 Solving -3.3 + t = -2.256102835 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + t = -2.256102835 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + t = -2.256102835 + 3.3 t = -2.256102835 + 3.3 Combine like terms: -2.256102835 + 3.3 = 1.043897165 t = 1.043897165 Simplifying t = 1.043897165Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.556102835, 1.043897165}
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