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Simplifying -16t2 + 200t + 5 = 0 Reorder the terms: 5 + 200t + -16t2 = 0 Solving 5 + 200t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + -12.5t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -12.5t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -12.5t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -12.5t + t2 = 0 + 0.3125 -12.5t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -12.5t + t2 = 0.3125 The t term is -12.5t. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5t + 39.0625 + t2 = 0.3125 + 39.0625 Reorder the terms: 39.0625 + -12.5t + t2 = 0.3125 + 39.0625 Combine like terms: 0.3125 + 39.0625 = 39.375 39.0625 + -12.5t + t2 = 39.375 Factor a perfect square on the left side: (t + -6.25)(t + -6.25) = 39.375 Calculate the square root of the right side: 6.274950199 Break this problem into two subproblems by setting (t + -6.25) equal to 6.274950199 and -6.274950199.Subproblem 1
t + -6.25 = 6.274950199 Simplifying t + -6.25 = 6.274950199 Reorder the terms: -6.25 + t = 6.274950199 Solving -6.25 + t = 6.274950199 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = 6.274950199 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = 6.274950199 + 6.25 t = 6.274950199 + 6.25 Combine like terms: 6.274950199 + 6.25 = 12.524950199 t = 12.524950199 Simplifying t = 12.524950199Subproblem 2
t + -6.25 = -6.274950199 Simplifying t + -6.25 = -6.274950199 Reorder the terms: -6.25 + t = -6.274950199 Solving -6.25 + t = -6.274950199 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + t = -6.274950199 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + t = -6.274950199 + 6.25 t = -6.274950199 + 6.25 Combine like terms: -6.274950199 + 6.25 = -0.024950199 t = -0.024950199 Simplifying t = -0.024950199Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.524950199, -0.024950199}
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