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Simplifying -5.9t2 + 55t + 36 = 0 Reorder the terms: 36 + 55t + -5.9t2 = 0 Solving 36 + 55t + -5.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5.9 the coefficient of the squared term: Divide each side by '-5.9'. -6.101694915 + -9.322033898t + t2 = 0 Move the constant term to the right: Add '6.101694915' to each side of the equation. -6.101694915 + -9.322033898t + 6.101694915 + t2 = 0 + 6.101694915 Reorder the terms: -6.101694915 + 6.101694915 + -9.322033898t + t2 = 0 + 6.101694915 Combine like terms: -6.101694915 + 6.101694915 = 0.000000000 0.000000000 + -9.322033898t + t2 = 0 + 6.101694915 -9.322033898t + t2 = 0 + 6.101694915 Combine like terms: 0 + 6.101694915 = 6.101694915 -9.322033898t + t2 = 6.101694915 The t term is -9.322033898t. Take half its coefficient (-4.661016949). Square it (21.72507900) and add it to both sides. Add '21.72507900' to each side of the equation. -9.322033898t + 21.72507900 + t2 = 6.101694915 + 21.72507900 Reorder the terms: 21.72507900 + -9.322033898t + t2 = 6.101694915 + 21.72507900 Combine like terms: 6.101694915 + 21.72507900 = 27.826773915 21.72507900 + -9.322033898t + t2 = 27.826773915 Factor a perfect square on the left side: (t + -4.661016949)(t + -4.661016949) = 27.826773915 Calculate the square root of the right side: 5.275108901 Break this problem into two subproblems by setting (t + -4.661016949) equal to 5.275108901 and -5.275108901.Subproblem 1
t + -4.661016949 = 5.275108901 Simplifying t + -4.661016949 = 5.275108901 Reorder the terms: -4.661016949 + t = 5.275108901 Solving -4.661016949 + t = 5.275108901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.661016949' to each side of the equation. -4.661016949 + 4.661016949 + t = 5.275108901 + 4.661016949 Combine like terms: -4.661016949 + 4.661016949 = 0.000000000 0.000000000 + t = 5.275108901 + 4.661016949 t = 5.275108901 + 4.661016949 Combine like terms: 5.275108901 + 4.661016949 = 9.93612585 t = 9.93612585 Simplifying t = 9.93612585Subproblem 2
t + -4.661016949 = -5.275108901 Simplifying t + -4.661016949 = -5.275108901 Reorder the terms: -4.661016949 + t = -5.275108901 Solving -4.661016949 + t = -5.275108901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.661016949' to each side of the equation. -4.661016949 + 4.661016949 + t = -5.275108901 + 4.661016949 Combine like terms: -4.661016949 + 4.661016949 = 0.000000000 0.000000000 + t = -5.275108901 + 4.661016949 t = -5.275108901 + 4.661016949 Combine like terms: -5.275108901 + 4.661016949 = -0.614091952 t = -0.614091952 Simplifying t = -0.614091952Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.93612585, -0.614091952}
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