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Simplifying -5t2 + -12t + 60 = 0 Reorder the terms: 60 + -12t + -5t2 = 0 Solving 60 + -12t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -12 + 2.4t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 2.4t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + 2.4t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2.4t + t2 = 0 + 12 2.4t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 2.4t + t2 = 12 The t term is 2.4t. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4t + 1.44 + t2 = 12 + 1.44 Reorder the terms: 1.44 + 2.4t + t2 = 12 + 1.44 Combine like terms: 12 + 1.44 = 13.44 1.44 + 2.4t + t2 = 13.44 Factor a perfect square on the left side: (t + 1.2)(t + 1.2) = 13.44 Calculate the square root of the right side: 3.666060556 Break this problem into two subproblems by setting (t + 1.2) equal to 3.666060556 and -3.666060556.Subproblem 1
t + 1.2 = 3.666060556 Simplifying t + 1.2 = 3.666060556 Reorder the terms: 1.2 + t = 3.666060556 Solving 1.2 + t = 3.666060556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + t = 3.666060556 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + t = 3.666060556 + -1.2 t = 3.666060556 + -1.2 Combine like terms: 3.666060556 + -1.2 = 2.466060556 t = 2.466060556 Simplifying t = 2.466060556Subproblem 2
t + 1.2 = -3.666060556 Simplifying t + 1.2 = -3.666060556 Reorder the terms: 1.2 + t = -3.666060556 Solving 1.2 + t = -3.666060556 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + t = -3.666060556 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + t = -3.666060556 + -1.2 t = -3.666060556 + -1.2 Combine like terms: -3.666060556 + -1.2 = -4.866060556 t = -4.866060556 Simplifying t = -4.866060556Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.466060556, -4.866060556}
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