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Simplifying 10t2 + -10t + 2.5 = 0 Reorder the terms: 2.5 + -10t + 10t2 = 0 Solving 2.5 + -10t + 10t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.25 + -1t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1t + t2 = 0 + -0.25 -1t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1t + t2 = -0.25 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = -0.25 + 0.25 Reorder the terms: 0.25 + -1t + t2 = -0.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.25 + -1t + t2 = 0.00 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (t + -0.5) equal to 0.00 and 0.00.Subproblem 1
t + -0.5 = 0.00 Simplifying t + -0.5 = 0.00 Reorder the terms: -0.5 + t = 0.00 Solving -0.5 + t = 0.00 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.00 + 0.5 t = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 t = 0.5 Simplifying t = 0.5Subproblem 2
t + -0.5 = 0.00 Simplifying t + -0.5 = 0.00 Reorder the terms: -0.5 + t = 0.00 Solving -0.5 + t = 0.00 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 0.00 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 0.00 + 0.5 t = 0.00 + 0.5 Combine like terms: 0.00 + 0.5 = 0.5 t = 0.5 Simplifying t = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.5, 0.5}
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