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Simplifying 2.5 = t(7 + -4.9t) 2.5 = (7 * t + -4.9t * t) 2.5 = (7t + -4.9t2) Solving 2.5 = 7t + -4.9t2 Solving for variable 't'. Reorder the terms: 2.5 + -7t + 4.9t2 = 7t + -7t + -4.9t2 + 4.9t2 Combine like terms: 7t + -7t = 0 2.5 + -7t + 4.9t2 = 0 + -4.9t2 + 4.9t2 2.5 + -7t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 2.5 + -7t + 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'. 0.5102040816 + -1.428571429t + t2 = 0 Move the constant term to the right: Add '-0.5102040816' to each side of the equation. 0.5102040816 + -1.428571429t + -0.5102040816 + t2 = 0 + -0.5102040816 Reorder the terms: 0.5102040816 + -0.5102040816 + -1.428571429t + t2 = 0 + -0.5102040816 Combine like terms: 0.5102040816 + -0.5102040816 = 0.0000000000 0.0000000000 + -1.428571429t + t2 = 0 + -0.5102040816 -1.428571429t + t2 = 0 + -0.5102040816 Combine like terms: 0 + -0.5102040816 = -0.5102040816 -1.428571429t + t2 = -0.5102040816 The t term is -1.428571429t. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429t + 0.5102040819 + t2 = -0.5102040816 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429t + t2 = -0.5102040816 + 0.5102040819 Combine like terms: -0.5102040816 + 0.5102040819 = 0.0000000003 0.5102040819 + -1.428571429t + t2 = 0.0000000003 Factor a perfect square on the left side: (t + -0.7142857145)(t + -0.7142857145) = 0.0000000003 Calculate the square root of the right side: 0.000017321 Break this problem into two subproblems by setting (t + -0.7142857145) equal to 0.000017321 and -0.000017321.Subproblem 1
t + -0.7142857145 = 0.000017321 Simplifying t + -0.7142857145 = 0.000017321 Reorder the terms: -0.7142857145 + t = 0.000017321 Solving -0.7142857145 + t = 0.000017321 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t = 0.000017321 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = 0.000017321 + 0.7142857145 t = 0.000017321 + 0.7142857145 Combine like terms: 0.000017321 + 0.7142857145 = 0.7143030355 t = 0.7143030355 Simplifying t = 0.7143030355Subproblem 2
t + -0.7142857145 = -0.000017321 Simplifying t + -0.7142857145 = -0.000017321 Reorder the terms: -0.7142857145 + t = -0.000017321 Solving -0.7142857145 + t = -0.000017321 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t = -0.000017321 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = -0.000017321 + 0.7142857145 t = -0.000017321 + 0.7142857145 Combine like terms: -0.000017321 + 0.7142857145 = 0.7142683935 t = 0.7142683935 Simplifying t = 0.7142683935Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.7143030355, 0.7142683935}
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