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Simplifying -4.9t2 + 4t + 250 = 0 Reorder the terms: 250 + 4t + -4.9t2 = 0 Solving 250 + 4t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -51.02040816 + -0.8163265306t + t2 = 0 Move the constant term to the right: Add '51.02040816' to each side of the equation. -51.02040816 + -0.8163265306t + 51.02040816 + t2 = 0 + 51.02040816 Reorder the terms: -51.02040816 + 51.02040816 + -0.8163265306t + t2 = 0 + 51.02040816 Combine like terms: -51.02040816 + 51.02040816 = 0.00000000 0.00000000 + -0.8163265306t + t2 = 0 + 51.02040816 -0.8163265306t + t2 = 0 + 51.02040816 Combine like terms: 0 + 51.02040816 = 51.02040816 -0.8163265306t + t2 = 51.02040816 The t term is -0.8163265306t. Take half its coefficient (-0.4081632653). Square it (0.1665972511) and add it to both sides. Add '0.1665972511' to each side of the equation. -0.8163265306t + 0.1665972511 + t2 = 51.02040816 + 0.1665972511 Reorder the terms: 0.1665972511 + -0.8163265306t + t2 = 51.02040816 + 0.1665972511 Combine like terms: 51.02040816 + 0.1665972511 = 51.1870054111 0.1665972511 + -0.8163265306t + t2 = 51.1870054111 Factor a perfect square on the left side: (t + -0.4081632653)(t + -0.4081632653) = 51.1870054111 Calculate the square root of the right side: 7.154509446 Break this problem into two subproblems by setting (t + -0.4081632653) equal to 7.154509446 and -7.154509446.Subproblem 1
t + -0.4081632653 = 7.154509446 Simplifying t + -0.4081632653 = 7.154509446 Reorder the terms: -0.4081632653 + t = 7.154509446 Solving -0.4081632653 + t = 7.154509446 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + t = 7.154509446 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = 7.154509446 + 0.4081632653 t = 7.154509446 + 0.4081632653 Combine like terms: 7.154509446 + 0.4081632653 = 7.5626727113 t = 7.5626727113 Simplifying t = 7.5626727113Subproblem 2
t + -0.4081632653 = -7.154509446 Simplifying t + -0.4081632653 = -7.154509446 Reorder the terms: -0.4081632653 + t = -7.154509446 Solving -0.4081632653 + t = -7.154509446 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4081632653' to each side of the equation. -0.4081632653 + 0.4081632653 + t = -7.154509446 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = -7.154509446 + 0.4081632653 t = -7.154509446 + 0.4081632653 Combine like terms: -7.154509446 + 0.4081632653 = -6.7463461807 t = -6.7463461807 Simplifying t = -6.7463461807Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.5626727113, -6.7463461807}
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