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Simplifying -4.9t2 + 35t + 40 = 0 Reorder the terms: 40 + 35t + -4.9t2 = 0 Solving 40 + 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'. -8.163265306 + -7.142857143t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -7.142857143t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -7.142857143t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -7.142857143t + t2 = 0 + 8.163265306 -7.142857143t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -7.142857143t + t2 = 8.163265306 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 = 8.163265306 + 12.75510204 Reorder the terms: 12.75510204 + -7.142857143t + t2 = 8.163265306 + 12.75510204 Combine like terms: 8.163265306 + 12.75510204 = 20.918367346 12.75510204 + -7.142857143t + t2 = 20.918367346 Factor a perfect square on the left side: (t + -3.571428572)(t + -3.571428572) = 20.918367346 Calculate the square root of the right side: 4.573660169 Break this problem into two subproblems by setting (t + -3.571428572) equal to 4.573660169 and -4.573660169.Subproblem 1
t + -3.571428572 = 4.573660169 Simplifying t + -3.571428572 = 4.573660169 Reorder the terms: -3.571428572 + t = 4.573660169 Solving -3.571428572 + t = 4.573660169 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 = 4.573660169 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = 4.573660169 + 3.571428572 t = 4.573660169 + 3.571428572 Combine like terms: 4.573660169 + 3.571428572 = 8.145088741 t = 8.145088741 Simplifying t = 8.145088741Subproblem 2
t + -3.571428572 = -4.573660169 Simplifying t + -3.571428572 = -4.573660169 Reorder the terms: -3.571428572 + t = -4.573660169 Solving -3.571428572 + t = -4.573660169 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 = -4.573660169 + 3.571428572 Combine like terms: -3.571428572 + 3.571428572 = 0.000000000 0.000000000 + t = -4.573660169 + 3.571428572 t = -4.573660169 + 3.571428572 Combine like terms: -4.573660169 + 3.571428572 = -1.002231597 t = -1.002231597 Simplifying t = -1.002231597Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.145088741, -1.002231597}
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