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Simplifying 9t2 + -95t + 200 = 0 Reorder the terms: 200 + -95t + 9t2 = 0 Solving 200 + -95t + 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'. 22.22222222 + -10.55555556t + t2 = 0 Move the constant term to the right: Add '-22.22222222' to each side of the equation. 22.22222222 + -10.55555556t + -22.22222222 + t2 = 0 + -22.22222222 Reorder the terms: 22.22222222 + -22.22222222 + -10.55555556t + t2 = 0 + -22.22222222 Combine like terms: 22.22222222 + -22.22222222 = 0.00000000 0.00000000 + -10.55555556t + t2 = 0 + -22.22222222 -10.55555556t + t2 = 0 + -22.22222222 Combine like terms: 0 + -22.22222222 = -22.22222222 -10.55555556t + t2 = -22.22222222 The t term is -10.55555556t. Take half its coefficient (-5.27777778). Square it (27.85493830) and add it to both sides. Add '27.85493830' to each side of the equation. -10.55555556t + 27.85493830 + t2 = -22.22222222 + 27.85493830 Reorder the terms: 27.85493830 + -10.55555556t + t2 = -22.22222222 + 27.85493830 Combine like terms: -22.22222222 + 27.85493830 = 5.63271608 27.85493830 + -10.55555556t + t2 = 5.63271608 Factor a perfect square on the left side: (t + -5.27777778)(t + -5.27777778) = 5.63271608 Calculate the square root of the right side: 2.37333438 Break this problem into two subproblems by setting (t + -5.27777778) equal to 2.37333438 and -2.37333438.Subproblem 1
t + -5.27777778 = 2.37333438 Simplifying t + -5.27777778 = 2.37333438 Reorder the terms: -5.27777778 + t = 2.37333438 Solving -5.27777778 + t = 2.37333438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.27777778' to each side of the equation. -5.27777778 + 5.27777778 + t = 2.37333438 + 5.27777778 Combine like terms: -5.27777778 + 5.27777778 = 0.00000000 0.00000000 + t = 2.37333438 + 5.27777778 t = 2.37333438 + 5.27777778 Combine like terms: 2.37333438 + 5.27777778 = 7.65111216 t = 7.65111216 Simplifying t = 7.65111216Subproblem 2
t + -5.27777778 = -2.37333438 Simplifying t + -5.27777778 = -2.37333438 Reorder the terms: -5.27777778 + t = -2.37333438 Solving -5.27777778 + t = -2.37333438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.27777778' to each side of the equation. -5.27777778 + 5.27777778 + t = -2.37333438 + 5.27777778 Combine like terms: -5.27777778 + 5.27777778 = 0.00000000 0.00000000 + t = -2.37333438 + 5.27777778 t = -2.37333438 + 5.27777778 Combine like terms: -2.37333438 + 5.27777778 = 2.9044434 t = 2.9044434 Simplifying t = 2.9044434Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.65111216, 2.9044434}
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