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Simplifying -4.9t2 + 68t + 2 = 0 Reorder the terms: 2 + 68t + -4.9t2 = 0 Solving 2 + 68t + -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'. -0.4081632653 + -13.87755102t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -13.87755102t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -13.87755102t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -13.87755102t + t2 = 0 + 0.4081632653 -13.87755102t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -13.87755102t + t2 = 0.4081632653 The t term is -13.87755102t. Take half its coefficient (-6.93877551). Square it (48.14660558) and add it to both sides. Add '48.14660558' to each side of the equation. -13.87755102t + 48.14660558 + t2 = 0.4081632653 + 48.14660558 Reorder the terms: 48.14660558 + -13.87755102t + t2 = 0.4081632653 + 48.14660558 Combine like terms: 0.4081632653 + 48.14660558 = 48.5547688453 48.14660558 + -13.87755102t + t2 = 48.5547688453 Factor a perfect square on the left side: (t + -6.93877551)(t + -6.93877551) = 48.5547688453 Calculate the square root of the right side: 6.968125203 Break this problem into two subproblems by setting (t + -6.93877551) equal to 6.968125203 and -6.968125203.Subproblem 1
t + -6.93877551 = 6.968125203 Simplifying t + -6.93877551 = 6.968125203 Reorder the terms: -6.93877551 + t = 6.968125203 Solving -6.93877551 + t = 6.968125203 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + t = 6.968125203 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + t = 6.968125203 + 6.93877551 t = 6.968125203 + 6.93877551 Combine like terms: 6.968125203 + 6.93877551 = 13.906900713 t = 13.906900713 Simplifying t = 13.906900713Subproblem 2
t + -6.93877551 = -6.968125203 Simplifying t + -6.93877551 = -6.968125203 Reorder the terms: -6.93877551 + t = -6.968125203 Solving -6.93877551 + t = -6.968125203 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.93877551' to each side of the equation. -6.93877551 + 6.93877551 + t = -6.968125203 + 6.93877551 Combine like terms: -6.93877551 + 6.93877551 = 0.00000000 0.00000000 + t = -6.968125203 + 6.93877551 t = -6.968125203 + 6.93877551 Combine like terms: -6.968125203 + 6.93877551 = -0.029349693 t = -0.029349693 Simplifying t = -0.029349693Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.906900713, -0.029349693}
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