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Simplifying 9t2 + -90t + 163 = 0 Reorder the terms: 163 + -90t + 9t2 = 0 Solving 163 + -90t + 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'. 18.11111111 + -10t + t2 = 0 Move the constant term to the right: Add '-18.11111111' to each side of the equation. 18.11111111 + -10t + -18.11111111 + t2 = 0 + -18.11111111 Reorder the terms: 18.11111111 + -18.11111111 + -10t + t2 = 0 + -18.11111111 Combine like terms: 18.11111111 + -18.11111111 = 0.00000000 0.00000000 + -10t + t2 = 0 + -18.11111111 -10t + t2 = 0 + -18.11111111 Combine like terms: 0 + -18.11111111 = -18.11111111 -10t + t2 = -18.11111111 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = -18.11111111 + 25 Reorder the terms: 25 + -10t + t2 = -18.11111111 + 25 Combine like terms: -18.11111111 + 25 = 6.88888889 25 + -10t + t2 = 6.88888889 Factor a perfect square on the left side: (t + -5)(t + -5) = 6.88888889 Calculate the square root of the right side: 2.624669292 Break this problem into two subproblems by setting (t + -5) equal to 2.624669292 and -2.624669292.Subproblem 1
t + -5 = 2.624669292 Simplifying t + -5 = 2.624669292 Reorder the terms: -5 + t = 2.624669292 Solving -5 + t = 2.624669292 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 2.624669292 + 5 Combine like terms: -5 + 5 = 0 0 + t = 2.624669292 + 5 t = 2.624669292 + 5 Combine like terms: 2.624669292 + 5 = 7.624669292 t = 7.624669292 Simplifying t = 7.624669292Subproblem 2
t + -5 = -2.624669292 Simplifying t + -5 = -2.624669292 Reorder the terms: -5 + t = -2.624669292 Solving -5 + t = -2.624669292 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -2.624669292 + 5 Combine like terms: -5 + 5 = 0 0 + t = -2.624669292 + 5 t = -2.624669292 + 5 Combine like terms: -2.624669292 + 5 = 2.375330708 t = 2.375330708 Simplifying t = 2.375330708Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.624669292, 2.375330708}
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