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Simplifying 0 = -16t2 + 160t + 80 Reorder the terms: 0 = 80 + 160t + -16t2 Solving 0 = 80 + 160t + -16t2 Solving for variable 't'. Combine like terms: 0 + -80 = -80 -80 + -160t + 16t2 = 80 + 160t + -16t2 + -80 + -160t + 16t2 Reorder the terms: -80 + -160t + 16t2 = 80 + -80 + 160t + -160t + -16t2 + 16t2 Combine like terms: 80 + -80 = 0 -80 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2 -80 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2 Combine like terms: 160t + -160t = 0 -80 + -160t + 16t2 = 0 + -16t2 + 16t2 -80 + -160t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -80 + -160t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-5 + -10t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-5 + -10t + t2)' equal to zero and attempt to solve: Simplifying -5 + -10t + t2 = 0 Solving -5 + -10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -10t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -10t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -10t + t2 = 0 + 5 -10t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -10t + t2 = 5 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 5 + 25 Reorder the terms: 25 + -10t + t2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + -10t + t2 = 30 Factor a perfect square on the left side: (t + -5)(t + -5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (t + -5) equal to 5.477225575 and -5.477225575.Subproblem 1
t + -5 = 5.477225575 Simplifying t + -5 = 5.477225575 Reorder the terms: -5 + t = 5.477225575 Solving -5 + t = 5.477225575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.477225575 + 5 t = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 t = 10.477225575 Simplifying t = 10.477225575Subproblem 2
t + -5 = -5.477225575 Simplifying t + -5 = -5.477225575 Reorder the terms: -5 + t = -5.477225575 Solving -5 + t = -5.477225575 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.477225575 + 5 t = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 t = -0.477225575 Simplifying t = -0.477225575Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.477225575, -0.477225575}Solution
t = {10.477225575, -0.477225575}
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