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Simplifying (4 + 5) * t2 + 4(4t) + 4(4) + -625 = 0 Combine like terms: 4 + 5 = 9 (9) * t2 + 4(4t) + 4(4) + -625 = 0 Remove parenthesis around (4t) 9t2 + 4 * 4t + 4(4) + -625 = 0 Multiply 4 * 4 9t2 + 16t + 4(4) + -625 = 0 Multiply 4 * 4 9t2 + 16t + 16 + -625 = 0 Reorder the terms: 16 + -625 + 16t + 9t2 = 0 Combine like terms: 16 + -625 = -609 -609 + 16t + 9t2 = 0 Solving -609 + 16t + 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'. -67.66666667 + 1.777777778t + t2 = 0 Move the constant term to the right: Add '67.66666667' to each side of the equation. -67.66666667 + 1.777777778t + 67.66666667 + t2 = 0 + 67.66666667 Reorder the terms: -67.66666667 + 67.66666667 + 1.777777778t + t2 = 0 + 67.66666667 Combine like terms: -67.66666667 + 67.66666667 = 0.00000000 0.00000000 + 1.777777778t + t2 = 0 + 67.66666667 1.777777778t + t2 = 0 + 67.66666667 Combine like terms: 0 + 67.66666667 = 67.66666667 1.777777778t + t2 = 67.66666667 The t term is 1.777777778t. Take half its coefficient (0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. 1.777777778t + 0.7901234570 + t2 = 67.66666667 + 0.7901234570 Reorder the terms: 0.7901234570 + 1.777777778t + t2 = 67.66666667 + 0.7901234570 Combine like terms: 67.66666667 + 0.7901234570 = 68.456790127 0.7901234570 + 1.777777778t + t2 = 68.456790127 Factor a perfect square on the left side: (t + 0.888888889)(t + 0.888888889) = 68.456790127 Calculate the square root of the right side: 8.273861863 Break this problem into two subproblems by setting (t + 0.888888889) equal to 8.273861863 and -8.273861863.Subproblem 1
t + 0.888888889 = 8.273861863 Simplifying t + 0.888888889 = 8.273861863 Reorder the terms: 0.888888889 + t = 8.273861863 Solving 0.888888889 + t = 8.273861863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + t = 8.273861863 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + t = 8.273861863 + -0.888888889 t = 8.273861863 + -0.888888889 Combine like terms: 8.273861863 + -0.888888889 = 7.384972974 t = 7.384972974 Simplifying t = 7.384972974Subproblem 2
t + 0.888888889 = -8.273861863 Simplifying t + 0.888888889 = -8.273861863 Reorder the terms: 0.888888889 + t = -8.273861863 Solving 0.888888889 + t = -8.273861863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.888888889' to each side of the equation. 0.888888889 + -0.888888889 + t = -8.273861863 + -0.888888889 Combine like terms: 0.888888889 + -0.888888889 = 0.000000000 0.000000000 + t = -8.273861863 + -0.888888889 t = -8.273861863 + -0.888888889 Combine like terms: -8.273861863 + -0.888888889 = -9.162750752 t = -9.162750752 Simplifying t = -9.162750752Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.384972974, -9.162750752}
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