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Simplifying (0.5t + -1)(0.5t + -1) = 0 Reorder the terms: (-1 + 0.5t)(0.5t + -1) = 0 Reorder the terms: (-1 + 0.5t)(-1 + 0.5t) = 0 Multiply (-1 + 0.5t) * (-1 + 0.5t) (-1(-1 + 0.5t) + 0.5t * (-1 + 0.5t)) = 0 ((-1 * -1 + 0.5t * -1) + 0.5t * (-1 + 0.5t)) = 0 ((1 + -0.5t) + 0.5t * (-1 + 0.5t)) = 0 (1 + -0.5t + (-1 * 0.5t + 0.5t * 0.5t)) = 0 (1 + -0.5t + (-0.5t + 0.25t2)) = 0 Combine like terms: -0.5t + -0.5t = -1t (1 + -1t + 0.25t2) = 0 Solving 1 + -1t + 0.25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 4 + -4t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -4t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4t + t2 = 0 + -4 -4t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4t + t2 = -4 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 = -4 + 4 Reorder the terms: 4 + -4t + t2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -4t + t2 = 0 Factor a perfect square on the left side: (t + -2)(t + -2) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (t + -2) equal to 0 and 0.Subproblem 1
t + -2 = 0 Simplifying t + -2 = 0 Reorder the terms: -2 + t = 0 Solving -2 + t = 0 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 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2Subproblem 2
t + -2 = 0 Simplifying t + -2 = 0 Reorder the terms: -2 + t = 0 Solving -2 + t = 0 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 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2Solution
The solution to the problem is based on the solutions from the subproblems. t = {2, 2}
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