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Simplifying 29 = 57t + -5t2 Solving 29 = 57t + -5t2 Solving for variable 't'. Reorder the terms: 29 + -57t + 5t2 = 57t + -57t + -5t2 + 5t2 Combine like terms: 57t + -57t = 0 29 + -57t + 5t2 = 0 + -5t2 + 5t2 29 + -57t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 29 + -57t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.8 + -11.4t + t2 = 0 Move the constant term to the right: Add '-5.8' to each side of the equation. 5.8 + -11.4t + -5.8 + t2 = 0 + -5.8 Reorder the terms: 5.8 + -5.8 + -11.4t + t2 = 0 + -5.8 Combine like terms: 5.8 + -5.8 = 0.0 0.0 + -11.4t + t2 = 0 + -5.8 -11.4t + t2 = 0 + -5.8 Combine like terms: 0 + -5.8 = -5.8 -11.4t + t2 = -5.8 The t term is -11.4t. Take half its coefficient (-5.7). Square it (32.49) and add it to both sides. Add '32.49' to each side of the equation. -11.4t + 32.49 + t2 = -5.8 + 32.49 Reorder the terms: 32.49 + -11.4t + t2 = -5.8 + 32.49 Combine like terms: -5.8 + 32.49 = 26.69 32.49 + -11.4t + t2 = 26.69 Factor a perfect square on the left side: (t + -5.7)(t + -5.7) = 26.69 Calculate the square root of the right side: 5.166236541 Break this problem into two subproblems by setting (t + -5.7) equal to 5.166236541 and -5.166236541.Subproblem 1
t + -5.7 = 5.166236541 Simplifying t + -5.7 = 5.166236541 Reorder the terms: -5.7 + t = 5.166236541 Solving -5.7 + t = 5.166236541 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.7' to each side of the equation. -5.7 + 5.7 + t = 5.166236541 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + t = 5.166236541 + 5.7 t = 5.166236541 + 5.7 Combine like terms: 5.166236541 + 5.7 = 10.866236541 t = 10.866236541 Simplifying t = 10.866236541Subproblem 2
t + -5.7 = -5.166236541 Simplifying t + -5.7 = -5.166236541 Reorder the terms: -5.7 + t = -5.166236541 Solving -5.7 + t = -5.166236541 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.7' to each side of the equation. -5.7 + 5.7 + t = -5.166236541 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + t = -5.166236541 + 5.7 t = -5.166236541 + 5.7 Combine like terms: -5.166236541 + 5.7 = 0.533763459 t = 0.533763459 Simplifying t = 0.533763459Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.866236541, 0.533763459}
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