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Simplifying -4.9t2 + 35t + 1 = 0 Reorder the terms: 1 + 35t + -4.9t2 = 0 Solving 1 + 35t + -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'. -0.2040816327 + -7.142857143t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -7.142857143t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -7.142857143t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -7.142857143t + t2 = 0 + 0.2040816327 -7.142857143t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -7.142857143t + t2 = 0.2040816327 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 = 0.2040816327 + 12.75510204 Reorder the terms: 12.75510204 + -7.142857143t + t2 = 0.2040816327 + 12.75510204 Combine like terms: 0.2040816327 + 12.75510204 = 12.9591836727 12.75510204 + -7.142857143t + t2 = 12.9591836727 Factor a perfect square on the left side: (t + -3.571428572)(t + -3.571428572) = 12.9591836727 Calculate the square root of the right side: 3.599886619 Break this problem into two subproblems by setting (t + -3.571428572) equal to 3.599886619 and -3.599886619.Subproblem 1
t + -3.571428572 = 3.599886619 Simplifying t + -3.571428572 = 3.599886619 Reorder the terms: -3.571428572 + t = 3.599886619 Solving -3.571428572 + t = 3.599886619 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 = 3.599886619 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = 3.599886619 + 3.571428572 t = 3.599886619 + 3.571428572 Combine like terms: 3.599886619 + 3.571428572 = 7.171315191 t = 7.171315191 Simplifying t = 7.171315191Subproblem 2
t + -3.571428572 = -3.599886619 Simplifying t + -3.571428572 = -3.599886619 Reorder the terms: -3.571428572 + t = -3.599886619 Solving -3.571428572 + t = -3.599886619 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 = -3.599886619 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = -3.599886619 + 3.571428572 t = -3.599886619 + 3.571428572 Combine like terms: -3.599886619 + 3.571428572 = -0.028458047 t = -0.028458047 Simplifying t = -0.028458047Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.171315191, -0.028458047}
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