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Simplifying 0 = -16t2 + 96t + 160 Reorder the terms: 0 = 160 + 96t + -16t2 Solving 0 = 160 + 96t + -16t2 Solving for variable 't'. Combine like terms: 0 + -160 = -160 -160 + -96t + 16t2 = 160 + 96t + -16t2 + -160 + -96t + 16t2 Reorder the terms: -160 + -96t + 16t2 = 160 + -160 + 96t + -96t + -16t2 + 16t2 Combine like terms: 160 + -160 = 0 -160 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2 -160 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2 Combine like terms: 96t + -96t = 0 -160 + -96t + 16t2 = 0 + -16t2 + 16t2 -160 + -96t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -160 + -96t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-10 + -6t + t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-10 + -6t + t2)' equal to zero and attempt to solve: Simplifying -10 + -6t + t2 = 0 Solving -10 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -6t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -6t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6t + t2 = 0 + 10 -6t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6t + t2 = 10 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 10 + 9 Reorder the terms: 9 + -6t + t2 = 10 + 9 Combine like terms: 10 + 9 = 19 9 + -6t + t2 = 19 Factor a perfect square on the left side: (t + -3)(t + -3) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (t + -3) equal to 4.358898944 and -4.358898944.Subproblem 1
t + -3 = 4.358898944 Simplifying t + -3 = 4.358898944 Reorder the terms: -3 + t = 4.358898944 Solving -3 + t = 4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.358898944 + 3 t = 4.358898944 + 3 Combine like terms: 4.358898944 + 3 = 7.358898944 t = 7.358898944 Simplifying t = 7.358898944Subproblem 2
t + -3 = -4.358898944 Simplifying t + -3 = -4.358898944 Reorder the terms: -3 + t = -4.358898944 Solving -3 + t = -4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.358898944 + 3 t = -4.358898944 + 3 Combine like terms: -4.358898944 + 3 = -1.358898944 t = -1.358898944 Simplifying t = -1.358898944Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.358898944, -1.358898944}Solution
t = {7.358898944, -1.358898944}
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