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Simplifying 9t2 + -200t + 776 = 0 Reorder the terms: 776 + -200t + 9t2 = 0 Solving 776 + -200t + 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'. 86.22222222 + -22.22222222t + t2 = 0 Move the constant term to the right: Add '-86.22222222' to each side of the equation. 86.22222222 + -22.22222222t + -86.22222222 + t2 = 0 + -86.22222222 Reorder the terms: 86.22222222 + -86.22222222 + -22.22222222t + t2 = 0 + -86.22222222 Combine like terms: 86.22222222 + -86.22222222 = 0.00000000 0.00000000 + -22.22222222t + t2 = 0 + -86.22222222 -22.22222222t + t2 = 0 + -86.22222222 Combine like terms: 0 + -86.22222222 = -86.22222222 -22.22222222t + t2 = -86.22222222 The t term is -22.22222222t. Take half its coefficient (-11.11111111). Square it (123.4567901) and add it to both sides. Add '123.4567901' to each side of the equation. -22.22222222t + 123.4567901 + t2 = -86.22222222 + 123.4567901 Reorder the terms: 123.4567901 + -22.22222222t + t2 = -86.22222222 + 123.4567901 Combine like terms: -86.22222222 + 123.4567901 = 37.23456788 123.4567901 + -22.22222222t + t2 = 37.23456788 Factor a perfect square on the left side: (t + -11.11111111)(t + -11.11111111) = 37.23456788 Calculate the square root of the right side: 6.102013428 Break this problem into two subproblems by setting (t + -11.11111111) equal to 6.102013428 and -6.102013428.Subproblem 1
t + -11.11111111 = 6.102013428 Simplifying t + -11.11111111 = 6.102013428 Reorder the terms: -11.11111111 + t = 6.102013428 Solving -11.11111111 + t = 6.102013428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + t = 6.102013428 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + t = 6.102013428 + 11.11111111 t = 6.102013428 + 11.11111111 Combine like terms: 6.102013428 + 11.11111111 = 17.213124538 t = 17.213124538 Simplifying t = 17.213124538Subproblem 2
t + -11.11111111 = -6.102013428 Simplifying t + -11.11111111 = -6.102013428 Reorder the terms: -11.11111111 + t = -6.102013428 Solving -11.11111111 + t = -6.102013428 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + t = -6.102013428 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + t = -6.102013428 + 11.11111111 t = -6.102013428 + 11.11111111 Combine like terms: -6.102013428 + 11.11111111 = 5.009097682 t = 5.009097682 Simplifying t = 5.009097682Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.213124538, 5.009097682}
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