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Simplifying 3 + 25t + -5t2 = 25 Solving 3 + 25t + -5t2 = 25 Solving for variable 't'. Reorder the terms: 3 + -25 + 25t + -5t2 = 25 + -25 Combine like terms: 3 + -25 = -22 -22 + 25t + -5t2 = 25 + -25 Combine like terms: 25 + -25 = 0 -22 + 25t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 4.4 + -5t + t2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + -5t + -4.4 + t2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + -5t + t2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + -5t + t2 = 0 + -4.4 -5t + t2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 -5t + t2 = -4.4 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = -4.4 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -4.4 + 6.25 Combine like terms: -4.4 + 6.25 = 1.85 6.25 + -5t + t2 = 1.85 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 1.85 Calculate the square root of the right side: 1.360147051 Break this problem into two subproblems by setting (t + -2.5) equal to 1.360147051 and -1.360147051.Subproblem 1
t + -2.5 = 1.360147051 Simplifying t + -2.5 = 1.360147051 Reorder the terms: -2.5 + t = 1.360147051 Solving -2.5 + t = 1.360147051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 1.360147051 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.360147051 + 2.5 t = 1.360147051 + 2.5 Combine like terms: 1.360147051 + 2.5 = 3.860147051 t = 3.860147051 Simplifying t = 3.860147051Subproblem 2
t + -2.5 = -1.360147051 Simplifying t + -2.5 = -1.360147051 Reorder the terms: -2.5 + t = -1.360147051 Solving -2.5 + t = -1.360147051 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -1.360147051 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.360147051 + 2.5 t = -1.360147051 + 2.5 Combine like terms: -1.360147051 + 2.5 = 1.139852949 t = 1.139852949 Simplifying t = 1.139852949Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.860147051, 1.139852949}
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