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Simplifying -180 = -16t2 + -14t Reorder the terms: -180 = -14t + -16t2 Solving -180 = -14t + -16t2 Solving for variable 't'. Reorder the terms: -180 + 14t + 16t2 = -14t + 14t + -16t2 + 16t2 Combine like terms: -14t + 14t = 0 -180 + 14t + 16t2 = 0 + -16t2 + 16t2 -180 + 14t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -180 + 14t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 7t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 7t + 8t2)' equal to zero and attempt to solve: Simplifying -90 + 7t + 8t2 = 0 Solving -90 + 7t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -11.25 + 0.875t + t2 = 0 Move the constant term to the right: Add '11.25' to each side of the equation. -11.25 + 0.875t + 11.25 + t2 = 0 + 11.25 Reorder the terms: -11.25 + 11.25 + 0.875t + t2 = 0 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + 0.875t + t2 = 0 + 11.25 0.875t + t2 = 0 + 11.25 Combine like terms: 0 + 11.25 = 11.25 0.875t + t2 = 11.25 The t term is 0.875t. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875t + 0.19140625 + t2 = 11.25 + 0.19140625 Reorder the terms: 0.19140625 + 0.875t + t2 = 11.25 + 0.19140625 Combine like terms: 11.25 + 0.19140625 = 11.44140625 0.19140625 + 0.875t + t2 = 11.44140625 Factor a perfect square on the left side: (t + 0.4375)(t + 0.4375) = 11.44140625 Calculate the square root of the right side: 3.382514782 Break this problem into two subproblems by setting (t + 0.4375) equal to 3.382514782 and -3.382514782.Subproblem 1
t + 0.4375 = 3.382514782 Simplifying t + 0.4375 = 3.382514782 Reorder the terms: 0.4375 + t = 3.382514782 Solving 0.4375 + t = 3.382514782 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + t = 3.382514782 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = 3.382514782 + -0.4375 t = 3.382514782 + -0.4375 Combine like terms: 3.382514782 + -0.4375 = 2.945014782 t = 2.945014782 Simplifying t = 2.945014782Subproblem 2
t + 0.4375 = -3.382514782 Simplifying t + 0.4375 = -3.382514782 Reorder the terms: 0.4375 + t = -3.382514782 Solving 0.4375 + t = -3.382514782 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + t = -3.382514782 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = -3.382514782 + -0.4375 t = -3.382514782 + -0.4375 Combine like terms: -3.382514782 + -0.4375 = -3.820014782 t = -3.820014782 Simplifying t = -3.820014782Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.945014782, -3.820014782}Solution
t = {2.945014782, -3.820014782}
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