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Simplifying 0 = 14t2 + 16t + 1798 Reorder the terms: 0 = 1798 + 16t + 14t2 Solving 0 = 1798 + 16t + 14t2 Solving for variable 't'. Combine like terms: 0 + -1798 = -1798 -1798 + -16t + -14t2 = 1798 + 16t + 14t2 + -1798 + -16t + -14t2 Reorder the terms: -1798 + -16t + -14t2 = 1798 + -1798 + 16t + -16t + 14t2 + -14t2 Combine like terms: 1798 + -1798 = 0 -1798 + -16t + -14t2 = 0 + 16t + -16t + 14t2 + -14t2 -1798 + -16t + -14t2 = 16t + -16t + 14t2 + -14t2 Combine like terms: 16t + -16t = 0 -1798 + -16t + -14t2 = 0 + 14t2 + -14t2 -1798 + -16t + -14t2 = 14t2 + -14t2 Combine like terms: 14t2 + -14t2 = 0 -1798 + -16t + -14t2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(899 + 8t + 7t2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(899 + 8t + 7t2)' equal to zero and attempt to solve: Simplifying 899 + 8t + 7t2 = 0 Solving 899 + 8t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 128.4285714 + 1.142857143t + t2 = 0 Move the constant term to the right: Add '-128.4285714' to each side of the equation. 128.4285714 + 1.142857143t + -128.4285714 + t2 = 0 + -128.4285714 Reorder the terms: 128.4285714 + -128.4285714 + 1.142857143t + t2 = 0 + -128.4285714 Combine like terms: 128.4285714 + -128.4285714 = 0.0000000 0.0000000 + 1.142857143t + t2 = 0 + -128.4285714 1.142857143t + t2 = 0 + -128.4285714 Combine like terms: 0 + -128.4285714 = -128.4285714 1.142857143t + t2 = -128.4285714 The t term is 1.142857143t. Take half its coefficient (0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. 1.142857143t + 0.3265306123 + t2 = -128.4285714 + 0.3265306123 Reorder the terms: 0.3265306123 + 1.142857143t + t2 = -128.4285714 + 0.3265306123 Combine like terms: -128.4285714 + 0.3265306123 = -128.1020407877 0.3265306123 + 1.142857143t + t2 = -128.1020407877 Factor a perfect square on the left side: (t + 0.5714285715)(t + 0.5714285715) = -128.1020407877 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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