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Simplifying 500 = 8t2 + -0.2t Reorder the terms: 500 = -0.2t + 8t2 Solving 500 = -0.2t + 8t2 Solving for variable 't'. Reorder the terms: 500 + 0.2t + -8t2 = -0.2t + 0.2t + 8t2 + -8t2 Combine like terms: -0.2t + 0.2t = 0.0 500 + 0.2t + -8t2 = 0.0 + 8t2 + -8t2 500 + 0.2t + -8t2 = 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 500 + 0.2t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -62.5 + -0.025t + t2 = 0 Move the constant term to the right: Add '62.5' to each side of the equation. -62.5 + -0.025t + 62.5 + t2 = 0 + 62.5 Reorder the terms: -62.5 + 62.5 + -0.025t + t2 = 0 + 62.5 Combine like terms: -62.5 + 62.5 = 0.0 0.0 + -0.025t + t2 = 0 + 62.5 -0.025t + t2 = 0 + 62.5 Combine like terms: 0 + 62.5 = 62.5 -0.025t + t2 = 62.5 The t term is -0.025t. Take half its coefficient (-0.0125). Square it (0.00015625) and add it to both sides. Add '0.00015625' to each side of the equation. -0.025t + 0.00015625 + t2 = 62.5 + 0.00015625 Reorder the terms: 0.00015625 + -0.025t + t2 = 62.5 + 0.00015625 Combine like terms: 62.5 + 0.00015625 = 62.50015625 0.00015625 + -0.025t + t2 = 62.50015625 Factor a perfect square on the left side: (t + -0.0125)(t + -0.0125) = 62.50015625 Calculate the square root of the right side: 7.905704033 Break this problem into two subproblems by setting (t + -0.0125) equal to 7.905704033 and -7.905704033.Subproblem 1
t + -0.0125 = 7.905704033 Simplifying t + -0.0125 = 7.905704033 Reorder the terms: -0.0125 + t = 7.905704033 Solving -0.0125 + t = 7.905704033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.0125' to each side of the equation. -0.0125 + 0.0125 + t = 7.905704033 + 0.0125 Combine like terms: -0.0125 + 0.0125 = 0.0000 0.0000 + t = 7.905704033 + 0.0125 t = 7.905704033 + 0.0125 Combine like terms: 7.905704033 + 0.0125 = 7.918204033 t = 7.918204033 Simplifying t = 7.918204033Subproblem 2
t + -0.0125 = -7.905704033 Simplifying t + -0.0125 = -7.905704033 Reorder the terms: -0.0125 + t = -7.905704033 Solving -0.0125 + t = -7.905704033 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.0125' to each side of the equation. -0.0125 + 0.0125 + t = -7.905704033 + 0.0125 Combine like terms: -0.0125 + 0.0125 = 0.0000 0.0000 + t = -7.905704033 + 0.0125 t = -7.905704033 + 0.0125 Combine like terms: -7.905704033 + 0.0125 = -7.893204033 t = -7.893204033 Simplifying t = -7.893204033Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.918204033, -7.893204033}
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