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Simplifying -15t2 + 60t + -44 = 0 Reorder the terms: -44 + 60t + -15t2 = 0 Solving -44 + 60t + -15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 2.933333333 + -4t + t2 = 0 Move the constant term to the right: Add '-2.933333333' to each side of the equation. 2.933333333 + -4t + -2.933333333 + t2 = 0 + -2.933333333 Reorder the terms: 2.933333333 + -2.933333333 + -4t + t2 = 0 + -2.933333333 Combine like terms: 2.933333333 + -2.933333333 = 0.000000000 0.000000000 + -4t + t2 = 0 + -2.933333333 -4t + t2 = 0 + -2.933333333 Combine like terms: 0 + -2.933333333 = -2.933333333 -4t + t2 = -2.933333333 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -2.933333333 + 4 Reorder the terms: 4 + -4t + t2 = -2.933333333 + 4 Combine like terms: -2.933333333 + 4 = 1.066666667 4 + -4t + t2 = 1.066666667 Factor a perfect square on the left side: (t + -2)(t + -2) = 1.066666667 Calculate the square root of the right side: 1.032795559 Break this problem into two subproblems by setting (t + -2) equal to 1.032795559 and -1.032795559.Subproblem 1
t + -2 = 1.032795559 Simplifying t + -2 = 1.032795559 Reorder the terms: -2 + t = 1.032795559 Solving -2 + t = 1.032795559 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.032795559 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.032795559 + 2 t = 1.032795559 + 2 Combine like terms: 1.032795559 + 2 = 3.032795559 t = 3.032795559 Simplifying t = 3.032795559Subproblem 2
t + -2 = -1.032795559 Simplifying t + -2 = -1.032795559 Reorder the terms: -2 + t = -1.032795559 Solving -2 + t = -1.032795559 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.032795559 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.032795559 + 2 t = -1.032795559 + 2 Combine like terms: -1.032795559 + 2 = 0.967204441 t = 0.967204441 Simplifying t = 0.967204441Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.032795559, 0.967204441}
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