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Simplifying 9t2 + -70t + 90 = 0 Reorder the terms: 90 + -70t + 9t2 = 0 Solving 90 + -70t + 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'. 10 + -7.777777778t + t2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -7.777777778t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + -7.777777778t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7.777777778t + t2 = 0 + -10 -7.777777778t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 -7.777777778t + t2 = -10 The t term is -7.777777778t. Take half its coefficient (-3.888888889). Square it (15.12345679) and add it to both sides. Add '15.12345679' to each side of the equation. -7.777777778t + 15.12345679 + t2 = -10 + 15.12345679 Reorder the terms: 15.12345679 + -7.777777778t + t2 = -10 + 15.12345679 Combine like terms: -10 + 15.12345679 = 5.12345679 15.12345679 + -7.777777778t + t2 = 5.12345679 Factor a perfect square on the left side: (t + -3.888888889)(t + -3.888888889) = 5.12345679 Calculate the square root of the right side: 2.263505421 Break this problem into two subproblems by setting (t + -3.888888889) equal to 2.263505421 and -2.263505421.Subproblem 1
t + -3.888888889 = 2.263505421 Simplifying t + -3.888888889 = 2.263505421 Reorder the terms: -3.888888889 + t = 2.263505421 Solving -3.888888889 + t = 2.263505421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.888888889' to each side of the equation. -3.888888889 + 3.888888889 + t = 2.263505421 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + t = 2.263505421 + 3.888888889 t = 2.263505421 + 3.888888889 Combine like terms: 2.263505421 + 3.888888889 = 6.15239431 t = 6.15239431 Simplifying t = 6.15239431Subproblem 2
t + -3.888888889 = -2.263505421 Simplifying t + -3.888888889 = -2.263505421 Reorder the terms: -3.888888889 + t = -2.263505421 Solving -3.888888889 + t = -2.263505421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.888888889' to each side of the equation. -3.888888889 + 3.888888889 + t = -2.263505421 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + t = -2.263505421 + 3.888888889 t = -2.263505421 + 3.888888889 Combine like terms: -2.263505421 + 3.888888889 = 1.625383468 t = 1.625383468 Simplifying t = 1.625383468Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.15239431, 1.625383468}
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