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Simplifying 4t + -0.8t2 = 2.5 Solving 4t + -0.8t2 = 2.5 Solving for variable 't'. Reorder the terms: -2.5 + 4t + -0.8t2 = 2.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + 4t + -0.8t2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 3.125 + -5t + t2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -5t + -3.125 + t2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -5t + t2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -5t + t2 = 0 + -3.125 -5t + t2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -5t + t2 = -3.125 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 = -3.125 + 6.25 Reorder the terms: 6.25 + -5t + t2 = -3.125 + 6.25 Combine like terms: -3.125 + 6.25 = 3.125 6.25 + -5t + t2 = 3.125 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (t + -2.5) equal to 1.767766953 and -1.767766953.Subproblem 1
t + -2.5 = 1.767766953 Simplifying t + -2.5 = 1.767766953 Reorder the terms: -2.5 + t = 1.767766953 Solving -2.5 + t = 1.767766953 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 = 1.767766953 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 1.767766953 + 2.5 t = 1.767766953 + 2.5 Combine like terms: 1.767766953 + 2.5 = 4.267766953 t = 4.267766953 Simplifying t = 4.267766953Subproblem 2
t + -2.5 = -1.767766953 Simplifying t + -2.5 = -1.767766953 Reorder the terms: -2.5 + t = -1.767766953 Solving -2.5 + t = -1.767766953 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 = -1.767766953 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -1.767766953 + 2.5 t = -1.767766953 + 2.5 Combine like terms: -1.767766953 + 2.5 = 0.732233047 t = 0.732233047 Simplifying t = 0.732233047Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.267766953, 0.732233047}
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