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Simplifying 1.5 + 4.0t + -0.5(9.8) * t2 = 0 Multiply -0.5 * 9.8 1.5 + 4.0t + -4.9t2 = 0 Solving 1.5 + 4.0t + -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'. -0.306122449 + -0.8163265306t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -0.8163265306t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -0.8163265306t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -0.8163265306t + t2 = 0 + 0.306122449 -0.8163265306t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -0.8163265306t + t2 = 0.306122449 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 = 0.306122449 + 0.1665972511 Reorder the terms: 0.1665972511 + -0.8163265306t + t2 = 0.306122449 + 0.1665972511 Combine like terms: 0.306122449 + 0.1665972511 = 0.4727197001 0.1665972511 + -0.8163265306t + t2 = 0.4727197001 Factor a perfect square on the left side: (t + -0.4081632653)(t + -0.4081632653) = 0.4727197001 Calculate the square root of the right side: 0.687546144 Break this problem into two subproblems by setting (t + -0.4081632653) equal to 0.687546144 and -0.687546144.Subproblem 1
t + -0.4081632653 = 0.687546144 Simplifying t + -0.4081632653 = 0.687546144 Reorder the terms: -0.4081632653 + t = 0.687546144 Solving -0.4081632653 + t = 0.687546144 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 = 0.687546144 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = 0.687546144 + 0.4081632653 t = 0.687546144 + 0.4081632653 Combine like terms: 0.687546144 + 0.4081632653 = 1.0957094093 t = 1.0957094093 Simplifying t = 1.0957094093Subproblem 2
t + -0.4081632653 = -0.687546144 Simplifying t + -0.4081632653 = -0.687546144 Reorder the terms: -0.4081632653 + t = -0.687546144 Solving -0.4081632653 + t = -0.687546144 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 = -0.687546144 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = -0.687546144 + 0.4081632653 t = -0.687546144 + 0.4081632653 Combine like terms: -0.687546144 + 0.4081632653 = -0.2793828787 t = -0.2793828787 Simplifying t = -0.2793828787Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.0957094093, -0.2793828787}
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