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Simplifying 9t2 + -30t + -4 = 0 Reorder the terms: -4 + -30t + 9t2 = 0 Solving -4 + -30t + 9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -3.333333333t + t2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -3.333333333t + 0.4444444444 + t2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -3.333333333t + t2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -3.333333333t + t2 = 0 + 0.4444444444 -3.333333333t + t2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -3.333333333t + t2 = 0.4444444444 The t term is -3.333333333t. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333t + 2.777777779 + t2 = 0.4444444444 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333t + t2 = 0.4444444444 + 2.777777779 Combine like terms: 0.4444444444 + 2.777777779 = 3.2222222234 2.777777779 + -3.333333333t + t2 = 3.2222222234 Factor a perfect square on the left side: (t + -1.666666667)(t + -1.666666667) = 3.2222222234 Calculate the square root of the right side: 1.795054936 Break this problem into two subproblems by setting (t + -1.666666667) equal to 1.795054936 and -1.795054936.Subproblem 1
t + -1.666666667 = 1.795054936 Simplifying t + -1.666666667 = 1.795054936 Reorder the terms: -1.666666667 + t = 1.795054936 Solving -1.666666667 + t = 1.795054936 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + t = 1.795054936 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + t = 1.795054936 + 1.666666667 t = 1.795054936 + 1.666666667 Combine like terms: 1.795054936 + 1.666666667 = 3.461721603 t = 3.461721603 Simplifying t = 3.461721603Subproblem 2
t + -1.666666667 = -1.795054936 Simplifying t + -1.666666667 = -1.795054936 Reorder the terms: -1.666666667 + t = -1.795054936 Solving -1.666666667 + t = -1.795054936 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + t = -1.795054936 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + t = -1.795054936 + 1.666666667 t = -1.795054936 + 1.666666667 Combine like terms: -1.795054936 + 1.666666667 = -0.128388269 t = -0.128388269 Simplifying t = -0.128388269Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.461721603, -0.128388269}
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