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Simplifying 0.0765t2 + -0.884t + 1.874 = 0 Reorder the terms: 1.874 + -0.884t + 0.0765t2 = 0 Solving 1.874 + -0.884t + 0.0765t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0765 the coefficient of the squared term: Divide each side by '0.0765'. 24.49673203 + -11.55555556t + t2 = 0 Move the constant term to the right: Add '-24.49673203' to each side of the equation. 24.49673203 + -11.55555556t + -24.49673203 + t2 = 0 + -24.49673203 Reorder the terms: 24.49673203 + -24.49673203 + -11.55555556t + t2 = 0 + -24.49673203 Combine like terms: 24.49673203 + -24.49673203 = 0.00000000 0.00000000 + -11.55555556t + t2 = 0 + -24.49673203 -11.55555556t + t2 = 0 + -24.49673203 Combine like terms: 0 + -24.49673203 = -24.49673203 -11.55555556t + t2 = -24.49673203 The t term is -11.55555556t. Take half its coefficient (-5.77777778). Square it (33.38271608) and add it to both sides. Add '33.38271608' to each side of the equation. -11.55555556t + 33.38271608 + t2 = -24.49673203 + 33.38271608 Reorder the terms: 33.38271608 + -11.55555556t + t2 = -24.49673203 + 33.38271608 Combine like terms: -24.49673203 + 33.38271608 = 8.88598405 33.38271608 + -11.55555556t + t2 = 8.88598405 Factor a perfect square on the left side: (t + -5.77777778)(t + -5.77777778) = 8.88598405 Calculate the square root of the right side: 2.980936774 Break this problem into two subproblems by setting (t + -5.77777778) equal to 2.980936774 and -2.980936774.Subproblem 1
t + -5.77777778 = 2.980936774 Simplifying t + -5.77777778 = 2.980936774 Reorder the terms: -5.77777778 + t = 2.980936774 Solving -5.77777778 + t = 2.980936774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.77777778' to each side of the equation. -5.77777778 + 5.77777778 + t = 2.980936774 + 5.77777778 Combine like terms: -5.77777778 + 5.77777778 = 0.00000000 0.00000000 + t = 2.980936774 + 5.77777778 t = 2.980936774 + 5.77777778 Combine like terms: 2.980936774 + 5.77777778 = 8.758714554 t = 8.758714554 Simplifying t = 8.758714554Subproblem 2
t + -5.77777778 = -2.980936774 Simplifying t + -5.77777778 = -2.980936774 Reorder the terms: -5.77777778 + t = -2.980936774 Solving -5.77777778 + t = -2.980936774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.77777778' to each side of the equation. -5.77777778 + 5.77777778 + t = -2.980936774 + 5.77777778 Combine like terms: -5.77777778 + 5.77777778 = 0.00000000 0.00000000 + t = -2.980936774 + 5.77777778 t = -2.980936774 + 5.77777778 Combine like terms: -2.980936774 + 5.77777778 = 2.796841006 t = 2.796841006 Simplifying t = 2.796841006Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.758714554, 2.796841006}
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