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Simplifying 0 = (-1t2) + 7t + 160 Reorder the terms: 0 = 160 + 7t + (-1t2) Solving 0 = 160 + 7t + (-1t2) Solving for variable 't'. 0 + -160 + -7t + t2 = 160 + 7t + (-1t2) + -160 + -7t + (t2) Combine like terms: 0 + -160 = -160 -160 + -7t + t2 = 160 + 7t + (-1t2) + -160 + -7t + (t2) -160 + -7t + t2 = 160 + 7t + (-1t2) + -160 + -7t + t2 Reorder the terms: -160 + -7t + t2 = 160 + -160 + 7t + -7t + (-1t2) + t2 Combine like terms: 160 + -160 = 0 -160 + -7t + t2 = 0 + 7t + -7t + (-1t2) + t2 -160 + -7t + t2 = 7t + -7t + (-1t2) + t2 Combine like terms: 7t + -7t = 0 -160 + -7t + t2 = 0 + (-1t2) + t2 -160 + -7t + t2 = (-1t2) + t2 Combine like terms: (-1t2) + t2 = 0 -160 + -7t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -7t + 160 + t2 = 0 + 160 Reorder the terms: -160 + 160 + -7t + t2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -7t + t2 = 0 + 160 -7t + t2 = 0 + 160 Combine like terms: 0 + 160 = 160 -7t + t2 = 160 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = 160 + 12.25 Reorder the terms: 12.25 + -7t + t2 = 160 + 12.25 Combine like terms: 160 + 12.25 = 172.25 12.25 + -7t + t2 = 172.25 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 172.25 Calculate the square root of the right side: 13.124404748 Break this problem into two subproblems by setting (t + -3.5) equal to 13.124404748 and -13.124404748.Subproblem 1
t + -3.5 = 13.124404748 Simplifying t + -3.5 = 13.124404748 Reorder the terms: -3.5 + t = 13.124404748 Solving -3.5 + t = 13.124404748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 13.124404748 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 13.124404748 + 3.5 t = 13.124404748 + 3.5 Combine like terms: 13.124404748 + 3.5 = 16.624404748 t = 16.624404748 Simplifying t = 16.624404748Subproblem 2
t + -3.5 = -13.124404748 Simplifying t + -3.5 = -13.124404748 Reorder the terms: -3.5 + t = -13.124404748 Solving -3.5 + t = -13.124404748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -13.124404748 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -13.124404748 + 3.5 t = -13.124404748 + 3.5 Combine like terms: -13.124404748 + 3.5 = -9.624404748 t = -9.624404748 Simplifying t = -9.624404748Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.624404748, -9.624404748}
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