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Simplifying -16t2 + 320t + 32 = 0 Reorder the terms: 32 + 320t + -16t2 = 0 Solving 32 + 320t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(2 + 20t + -1t2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(2 + 20t + -1t2)' equal to zero and attempt to solve: Simplifying 2 + 20t + -1t2 = 0 Solving 2 + 20t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -20t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -20t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -20t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -20t + t2 = 0 + 2 -20t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -20t + t2 = 2 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 2 + 100 Reorder the terms: 100 + -20t + t2 = 2 + 100 Combine like terms: 2 + 100 = 102 100 + -20t + t2 = 102 Factor a perfect square on the left side: (t + -10)(t + -10) = 102 Calculate the square root of the right side: 10.099504938 Break this problem into two subproblems by setting (t + -10) equal to 10.099504938 and -10.099504938.Subproblem 1
t + -10 = 10.099504938 Simplifying t + -10 = 10.099504938 Reorder the terms: -10 + t = 10.099504938 Solving -10 + t = 10.099504938 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 10.099504938 + 10 Combine like terms: -10 + 10 = 0 0 + t = 10.099504938 + 10 t = 10.099504938 + 10 Combine like terms: 10.099504938 + 10 = 20.099504938 t = 20.099504938 Simplifying t = 20.099504938Subproblem 2
t + -10 = -10.099504938 Simplifying t + -10 = -10.099504938 Reorder the terms: -10 + t = -10.099504938 Solving -10 + t = -10.099504938 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -10.099504938 + 10 Combine like terms: -10 + 10 = 0 0 + t = -10.099504938 + 10 t = -10.099504938 + 10 Combine like terms: -10.099504938 + 10 = -0.099504938 t = -0.099504938 Simplifying t = -0.099504938Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.099504938, -0.099504938}Solution
t = {20.099504938, -0.099504938}
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