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Simplifying 5t2 + -18t + -3 = 0 Reorder the terms: -3 + -18t + 5t2 = 0 Solving -3 + -18t + 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'. -0.6 + -3.6t + t2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -3.6t + 0.6 + t2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -3.6t + t2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -3.6t + t2 = 0 + 0.6 -3.6t + t2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -3.6t + t2 = 0.6 The t term is -3.6t. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6t + 3.24 + t2 = 0.6 + 3.24 Reorder the terms: 3.24 + -3.6t + t2 = 0.6 + 3.24 Combine like terms: 0.6 + 3.24 = 3.84 3.24 + -3.6t + t2 = 3.84 Factor a perfect square on the left side: (t + -1.8)(t + -1.8) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (t + -1.8) equal to 1.959591794 and -1.959591794.Subproblem 1
t + -1.8 = 1.959591794 Simplifying t + -1.8 = 1.959591794 Reorder the terms: -1.8 + t = 1.959591794 Solving -1.8 + t = 1.959591794 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + t = 1.959591794 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + t = 1.959591794 + 1.8 t = 1.959591794 + 1.8 Combine like terms: 1.959591794 + 1.8 = 3.759591794 t = 3.759591794 Simplifying t = 3.759591794Subproblem 2
t + -1.8 = -1.959591794 Simplifying t + -1.8 = -1.959591794 Reorder the terms: -1.8 + t = -1.959591794 Solving -1.8 + t = -1.959591794 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + t = -1.959591794 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + t = -1.959591794 + 1.8 t = -1.959591794 + 1.8 Combine like terms: -1.959591794 + 1.8 = -0.159591794 t = -0.159591794 Simplifying t = -0.159591794Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.759591794, -0.159591794}
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