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Simplifying 4t2 + 0.33t + -5 = 0 Reorder the terms: -5 + 0.33t + 4t2 = 0 Solving -5 + 0.33t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 0.0825t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.0825t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.0825t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.0825t + t2 = 0 + 1.25 0.0825t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.0825t + t2 = 1.25 The t term is 0.0825t. Take half its coefficient (0.04125). Square it (0.0017015625) and add it to both sides. Add '0.0017015625' to each side of the equation. 0.0825t + 0.0017015625 + t2 = 1.25 + 0.0017015625 Reorder the terms: 0.0017015625 + 0.0825t + t2 = 1.25 + 0.0017015625 Combine like terms: 1.25 + 0.0017015625 = 1.2517015625 0.0017015625 + 0.0825t + t2 = 1.2517015625 Factor a perfect square on the left side: (t + 0.04125)(t + 0.04125) = 1.2517015625 Calculate the square root of the right side: 1.118794692 Break this problem into two subproblems by setting (t + 0.04125) equal to 1.118794692 and -1.118794692.Subproblem 1
t + 0.04125 = 1.118794692 Simplifying t + 0.04125 = 1.118794692 Reorder the terms: 0.04125 + t = 1.118794692 Solving 0.04125 + t = 1.118794692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.04125' to each side of the equation. 0.04125 + -0.04125 + t = 1.118794692 + -0.04125 Combine like terms: 0.04125 + -0.04125 = 0.00000 0.00000 + t = 1.118794692 + -0.04125 t = 1.118794692 + -0.04125 Combine like terms: 1.118794692 + -0.04125 = 1.077544692 t = 1.077544692 Simplifying t = 1.077544692Subproblem 2
t + 0.04125 = -1.118794692 Simplifying t + 0.04125 = -1.118794692 Reorder the terms: 0.04125 + t = -1.118794692 Solving 0.04125 + t = -1.118794692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.04125' to each side of the equation. 0.04125 + -0.04125 + t = -1.118794692 + -0.04125 Combine like terms: 0.04125 + -0.04125 = 0.00000 0.00000 + t = -1.118794692 + -0.04125 t = -1.118794692 + -0.04125 Combine like terms: -1.118794692 + -0.04125 = -1.160044692 t = -1.160044692 Simplifying t = -1.160044692Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.077544692, -1.160044692}
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