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Simplifying t2 + -3t = -2.25 Reorder the terms: -3t + t2 = -2.25 Solving -3t + t2 = -2.25 Solving for variable 't'. Reorder the terms: 2.25 + -3t + t2 = -2.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 2.25 + -3t + t2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -3t + -2.25 + t2 = 0.00 + -2.25 Reorder the terms: 2.25 + -2.25 + -3t + t2 = 0.00 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -3t + t2 = 0.00 + -2.25 -3t + t2 = 0.00 + -2.25 Combine like terms: 0.00 + -2.25 = -2.25 -3t + t2 = -2.25 The t term is -3t. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3t + 2.25 + t2 = -2.25 + 2.25 Reorder the terms: 2.25 + -3t + t2 = -2.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 2.25 + -3t + t2 = 0.00 Factor a perfect square on the left side: (t + -1.5)(t + -1.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (t + -1.5) equal to 0.00 and 0.00.Subproblem 1
t + -1.5 = 0.00 Simplifying t + -1.5 = 0.00 Reorder the terms: -1.5 + t = 0.00 Solving -1.5 + t = 0.00 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 0.00 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 0.00 + 1.5 t = 0.00 + 1.5 Combine like terms: 0.00 + 1.5 = 1.5 t = 1.5 Simplifying t = 1.5Subproblem 2
t + -1.5 = 0.00 Simplifying t + -1.5 = 0.00 Reorder the terms: -1.5 + t = 0.00 Solving -1.5 + t = 0.00 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 0.00 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 0.00 + 1.5 t = 0.00 + 1.5 Combine like terms: 0.00 + 1.5 = 1.5 t = 1.5 Simplifying t = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.5, 1.5}
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