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Simplifying 9t2 + 24t + 4096 = 0 Reorder the terms: 4096 + 24t + 9t2 = 0 Solving 4096 + 24t + 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'. 455.1111111 + 2.666666667t + t2 = 0 Move the constant term to the right: Add '-455.1111111' to each side of the equation. 455.1111111 + 2.666666667t + -455.1111111 + t2 = 0 + -455.1111111 Reorder the terms: 455.1111111 + -455.1111111 + 2.666666667t + t2 = 0 + -455.1111111 Combine like terms: 455.1111111 + -455.1111111 = 0.0000000 0.0000000 + 2.666666667t + t2 = 0 + -455.1111111 2.666666667t + t2 = 0 + -455.1111111 Combine like terms: 0 + -455.1111111 = -455.1111111 2.666666667t + t2 = -455.1111111 The t term is 2.666666667t. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667t + 1.777777780 + t2 = -455.1111111 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667t + t2 = -455.1111111 + 1.777777780 Combine like terms: -455.1111111 + 1.777777780 = -453.33333332 1.777777780 + 2.666666667t + t2 = -453.33333332 Factor a perfect square on the left side: (t + 1.333333334)(t + 1.333333334) = -453.33333332 Can't calculate square root of the right side. The solution to this equation could not be determined.
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