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Simplifying 5t * t + -12t + -12 = 0 Multiply t * t 5t2 + -12t + -12 = 0 Reorder the terms: -12 + -12t + 5t2 = 0 Solving -12 + -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'. -2.4 + -2.4t + t2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -2.4t + 2.4 + t2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -2.4t + t2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -2.4t + t2 = 0 + 2.4 -2.4t + t2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -2.4t + t2 = 2.4 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 = 2.4 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = 2.4 + 1.44 Combine like terms: 2.4 + 1.44 = 3.84 1.44 + -2.4t + t2 = 3.84 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (t + -1.2) equal to 1.959591794 and -1.959591794.Subproblem 1
t + -1.2 = 1.959591794 Simplifying t + -1.2 = 1.959591794 Reorder the terms: -1.2 + t = 1.959591794 Solving -1.2 + t = 1.959591794 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 = 1.959591794 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 1.959591794 + 1.2 t = 1.959591794 + 1.2 Combine like terms: 1.959591794 + 1.2 = 3.159591794 t = 3.159591794 Simplifying t = 3.159591794Subproblem 2
t + -1.2 = -1.959591794 Simplifying t + -1.2 = -1.959591794 Reorder the terms: -1.2 + t = -1.959591794 Solving -1.2 + t = -1.959591794 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 = -1.959591794 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -1.959591794 + 1.2 t = -1.959591794 + 1.2 Combine like terms: -1.959591794 + 1.2 = -0.759591794 t = -0.759591794 Simplifying t = -0.759591794Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.159591794, -0.759591794}
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