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Simplifying -4.9t2 + 4t + 3 = 0 Reorder the terms: 3 + 4t + -4.9t2 = 0 Solving 3 + 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'. -0.612244898 + -0.8163265306t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -0.8163265306t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -0.8163265306t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -0.8163265306t + t2 = 0 + 0.612244898 -0.8163265306t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -0.8163265306t + t2 = 0.612244898 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 = 0.612244898 + 0.1665972511 Reorder the terms: 0.1665972511 + -0.8163265306t + t2 = 0.612244898 + 0.1665972511 Combine like terms: 0.612244898 + 0.1665972511 = 0.7788421491 0.1665972511 + -0.8163265306t + t2 = 0.7788421491 Factor a perfect square on the left side: (t + -0.4081632653)(t + -0.4081632653) = 0.7788421491 Calculate the square root of the right side: 0.882520339 Break this problem into two subproblems by setting (t + -0.4081632653) equal to 0.882520339 and -0.882520339.Subproblem 1
t + -0.4081632653 = 0.882520339 Simplifying t + -0.4081632653 = 0.882520339 Reorder the terms: -0.4081632653 + t = 0.882520339 Solving -0.4081632653 + t = 0.882520339 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 = 0.882520339 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = 0.882520339 + 0.4081632653 t = 0.882520339 + 0.4081632653 Combine like terms: 0.882520339 + 0.4081632653 = 1.2906836043 t = 1.2906836043 Simplifying t = 1.2906836043Subproblem 2
t + -0.4081632653 = -0.882520339 Simplifying t + -0.4081632653 = -0.882520339 Reorder the terms: -0.4081632653 + t = -0.882520339 Solving -0.4081632653 + t = -0.882520339 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 = -0.882520339 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + t = -0.882520339 + 0.4081632653 t = -0.882520339 + 0.4081632653 Combine like terms: -0.882520339 + 0.4081632653 = -0.4743570737 t = -0.4743570737 Simplifying t = -0.4743570737Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.2906836043, -0.4743570737}
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