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Simplifying 16t2 + 1120t + 7280 = 0 Reorder the terms: 7280 + 1120t + 16t2 = 0 Solving 7280 + 1120t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(455 + 70t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(455 + 70t + t2)' equal to zero and attempt to solve: Simplifying 455 + 70t + t2 = 0 Solving 455 + 70t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-455' to each side of the equation. 455 + 70t + -455 + t2 = 0 + -455 Reorder the terms: 455 + -455 + 70t + t2 = 0 + -455 Combine like terms: 455 + -455 = 0 0 + 70t + t2 = 0 + -455 70t + t2 = 0 + -455 Combine like terms: 0 + -455 = -455 70t + t2 = -455 The t term is 70t. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70t + 1225 + t2 = -455 + 1225 Reorder the terms: 1225 + 70t + t2 = -455 + 1225 Combine like terms: -455 + 1225 = 770 1225 + 70t + t2 = 770 Factor a perfect square on the left side: (t + 35)(t + 35) = 770 Calculate the square root of the right side: 27.748873851 Break this problem into two subproblems by setting (t + 35) equal to 27.748873851 and -27.748873851.Subproblem 1
t + 35 = 27.748873851 Simplifying t + 35 = 27.748873851 Reorder the terms: 35 + t = 27.748873851 Solving 35 + t = 27.748873851 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + t = 27.748873851 + -35 Combine like terms: 35 + -35 = 0 0 + t = 27.748873851 + -35 t = 27.748873851 + -35 Combine like terms: 27.748873851 + -35 = -7.251126149 t = -7.251126149 Simplifying t = -7.251126149Subproblem 2
t + 35 = -27.748873851 Simplifying t + 35 = -27.748873851 Reorder the terms: 35 + t = -27.748873851 Solving 35 + t = -27.748873851 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + t = -27.748873851 + -35 Combine like terms: 35 + -35 = 0 0 + t = -27.748873851 + -35 t = -27.748873851 + -35 Combine like terms: -27.748873851 + -35 = -62.748873851 t = -62.748873851 Simplifying t = -62.748873851Solution
The solution to the problem is based on the solutions from the subproblems. t = {-7.251126149, -62.748873851}Solution
t = {-7.251126149, -62.748873851}
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