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Simplifying 0 = -16t2 + -10t + 190 Reorder the terms: 0 = 190 + -10t + -16t2 Solving 0 = 190 + -10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -190 = -190 -190 + 10t + 16t2 = 190 + -10t + -16t2 + -190 + 10t + 16t2 Reorder the terms: -190 + 10t + 16t2 = 190 + -190 + -10t + 10t + -16t2 + 16t2 Combine like terms: 190 + -190 = 0 -190 + 10t + 16t2 = 0 + -10t + 10t + -16t2 + 16t2 -190 + 10t + 16t2 = -10t + 10t + -16t2 + 16t2 Combine like terms: -10t + 10t = 0 -190 + 10t + 16t2 = 0 + -16t2 + 16t2 -190 + 10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -190 + 10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + 5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying -95 + 5t + 8t2 = 0 Solving -95 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.875 + 0.625t + t2 = 0 Move the constant term to the right: Add '11.875' to each side of the equation. -11.875 + 0.625t + 11.875 + t2 = 0 + 11.875 Reorder the terms: -11.875 + 11.875 + 0.625t + t2 = 0 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + 0.625t + t2 = 0 + 11.875 0.625t + t2 = 0 + 11.875 Combine like terms: 0 + 11.875 = 11.875 0.625t + t2 = 11.875 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 11.875 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 11.875 + 0.09765625 Combine like terms: 11.875 + 0.09765625 = 11.97265625 0.09765625 + 0.625t + t2 = 11.97265625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 11.97265625 Calculate the square root of the right side: 3.460152634 Break this problem into two subproblems by setting (t + 0.3125) equal to 3.460152634 and -3.460152634.Subproblem 1
t + 0.3125 = 3.460152634 Simplifying t + 0.3125 = 3.460152634 Reorder the terms: 0.3125 + t = 3.460152634 Solving 0.3125 + t = 3.460152634 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 3.460152634 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 3.460152634 + -0.3125 t = 3.460152634 + -0.3125 Combine like terms: 3.460152634 + -0.3125 = 3.147652634 t = 3.147652634 Simplifying t = 3.147652634Subproblem 2
t + 0.3125 = -3.460152634 Simplifying t + 0.3125 = -3.460152634 Reorder the terms: 0.3125 + t = -3.460152634 Solving 0.3125 + t = -3.460152634 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -3.460152634 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -3.460152634 + -0.3125 t = -3.460152634 + -0.3125 Combine like terms: -3.460152634 + -0.3125 = -3.772652634 t = -3.772652634 Simplifying t = -3.772652634Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.147652634, -3.772652634}Solution
t = {3.147652634, -3.772652634}
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