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Simplifying 0 = -4.9t2 + -35t + 21 Reorder the terms: 0 = 21 + -35t + -4.9t2 Solving 0 = 21 + -35t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -21 = -21 -21 + 35t + 4.9t2 = 21 + -35t + -4.9t2 + -21 + 35t + 4.9t2 Reorder the terms: -21 + 35t + 4.9t2 = 21 + -21 + -35t + 35t + -4.9t2 + 4.9t2 Combine like terms: 21 + -21 = 0 -21 + 35t + 4.9t2 = 0 + -35t + 35t + -4.9t2 + 4.9t2 -21 + 35t + 4.9t2 = -35t + 35t + -4.9t2 + 4.9t2 Combine like terms: -35t + 35t = 0 -21 + 35t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -21 + 35t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -21 + 35t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.285714286 + 7.142857143t + t2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 7.142857143t + 4.285714286 + t2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 7.142857143t + t2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 7.142857143t + t2 = 0 + 4.285714286 7.142857143t + t2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 7.142857143t + t2 = 4.285714286 The t term is 7.142857143t. Take half its coefficient (3.571428572). Square it (12.75510204) and add it to both sides. Add '12.75510204' to each side of the equation. 7.142857143t + 12.75510204 + t2 = 4.285714286 + 12.75510204 Reorder the terms: 12.75510204 + 7.142857143t + t2 = 4.285714286 + 12.75510204 Combine like terms: 4.285714286 + 12.75510204 = 17.040816326 12.75510204 + 7.142857143t + t2 = 17.040816326 Factor a perfect square on the left side: (t + 3.571428572)(t + 3.571428572) = 17.040816326 Calculate the square root of the right side: 4.128052365 Break this problem into two subproblems by setting (t + 3.571428572) equal to 4.128052365 and -4.128052365.Subproblem 1
t + 3.571428572 = 4.128052365 Simplifying t + 3.571428572 = 4.128052365 Reorder the terms: 3.571428572 + t = 4.128052365 Solving 3.571428572 + t = 4.128052365 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + t = 4.128052365 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + t = 4.128052365 + -3.571428572 t = 4.128052365 + -3.571428572 Combine like terms: 4.128052365 + -3.571428572 = 0.556623793 t = 0.556623793 Simplifying t = 0.556623793Subproblem 2
t + 3.571428572 = -4.128052365 Simplifying t + 3.571428572 = -4.128052365 Reorder the terms: 3.571428572 + t = -4.128052365 Solving 3.571428572 + t = -4.128052365 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.571428572' to each side of the equation. 3.571428572 + -3.571428572 + t = -4.128052365 + -3.571428572 Combine like terms: 3.571428572 + -3.571428572 = 0.000000000 0.000000000 + t = -4.128052365 + -3.571428572 t = -4.128052365 + -3.571428572 Combine like terms: -4.128052365 + -3.571428572 = -7.699480937 t = -7.699480937 Simplifying t = -7.699480937Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.556623793, -7.699480937}
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