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Simplifying 39 = -16t2 + 122t + 131 Reorder the terms: 39 = 131 + 122t + -16t2 Solving 39 = 131 + 122t + -16t2 Solving for variable 't'. Combine like terms: 39 + -131 = -92 -92 + -122t + 16t2 = 131 + 122t + -16t2 + -131 + -122t + 16t2 Reorder the terms: -92 + -122t + 16t2 = 131 + -131 + 122t + -122t + -16t2 + 16t2 Combine like terms: 131 + -131 = 0 -92 + -122t + 16t2 = 0 + 122t + -122t + -16t2 + 16t2 -92 + -122t + 16t2 = 122t + -122t + -16t2 + 16t2 Combine like terms: 122t + -122t = 0 -92 + -122t + 16t2 = 0 + -16t2 + 16t2 -92 + -122t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -92 + -122t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-46 + -61t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-46 + -61t + 8t2)' equal to zero and attempt to solve: Simplifying -46 + -61t + 8t2 = 0 Solving -46 + -61t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.75 + -7.625t + t2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -7.625t + 5.75 + t2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -7.625t + t2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -7.625t + t2 = 0 + 5.75 -7.625t + t2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -7.625t + t2 = 5.75 The t term is -7.625t. Take half its coefficient (-3.8125). Square it (14.53515625) and add it to both sides. Add '14.53515625' to each side of the equation. -7.625t + 14.53515625 + t2 = 5.75 + 14.53515625 Reorder the terms: 14.53515625 + -7.625t + t2 = 5.75 + 14.53515625 Combine like terms: 5.75 + 14.53515625 = 20.28515625 14.53515625 + -7.625t + t2 = 20.28515625 Factor a perfect square on the left side: (t + -3.8125)(t + -3.8125) = 20.28515625 Calculate the square root of the right side: 4.503904556 Break this problem into two subproblems by setting (t + -3.8125) equal to 4.503904556 and -4.503904556.Subproblem 1
t + -3.8125 = 4.503904556 Simplifying t + -3.8125 = 4.503904556 Reorder the terms: -3.8125 + t = 4.503904556 Solving -3.8125 + t = 4.503904556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = 4.503904556 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = 4.503904556 + 3.8125 t = 4.503904556 + 3.8125 Combine like terms: 4.503904556 + 3.8125 = 8.316404556 t = 8.316404556 Simplifying t = 8.316404556Subproblem 2
t + -3.8125 = -4.503904556 Simplifying t + -3.8125 = -4.503904556 Reorder the terms: -3.8125 + t = -4.503904556 Solving -3.8125 + t = -4.503904556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8125' to each side of the equation. -3.8125 + 3.8125 + t = -4.503904556 + 3.8125 Combine like terms: -3.8125 + 3.8125 = 0.0000 0.0000 + t = -4.503904556 + 3.8125 t = -4.503904556 + 3.8125 Combine like terms: -4.503904556 + 3.8125 = -0.691404556 t = -0.691404556 Simplifying t = -0.691404556Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.316404556, -0.691404556}Solution
t = {8.316404556, -0.691404556}
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