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Simplifying 2 = t(28 + -4.9t) 2 = (28 * t + -4.9t * t) 2 = (28t + -4.9t2) Solving 2 = 28t + -4.9t2 Solving for variable 't'. Reorder the terms: 2 + -28t + 4.9t2 = 28t + -28t + -4.9t2 + 4.9t2 Combine like terms: 28t + -28t = 0 2 + -28t + 4.9t2 = 0 + -4.9t2 + 4.9t2 2 + -28t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 2 + -28t + 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'. 0.4081632653 + -5.714285714t + t2 = 0 Move the constant term to the right: Add '-0.4081632653' to each side of the equation. 0.4081632653 + -5.714285714t + -0.4081632653 + t2 = 0 + -0.4081632653 Reorder the terms: 0.4081632653 + -0.4081632653 + -5.714285714t + t2 = 0 + -0.4081632653 Combine like terms: 0.4081632653 + -0.4081632653 = 0.0000000000 0.0000000000 + -5.714285714t + t2 = 0 + -0.4081632653 -5.714285714t + t2 = 0 + -0.4081632653 Combine like terms: 0 + -0.4081632653 = -0.4081632653 -5.714285714t + t2 = -0.4081632653 The t term is -5.714285714t. Take half its coefficient (-2.857142857). Square it (8.163265305) and add it to both sides. Add '8.163265305' to each side of the equation. -5.714285714t + 8.163265305 + t2 = -0.4081632653 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714t + t2 = -0.4081632653 + 8.163265305 Combine like terms: -0.4081632653 + 8.163265305 = 7.7551020397 8.163265305 + -5.714285714t + t2 = 7.7551020397 Factor a perfect square on the left side: (t + -2.857142857)(t + -2.857142857) = 7.7551020397 Calculate the square root of the right side: 2.784798384 Break this problem into two subproblems by setting (t + -2.857142857) equal to 2.784798384 and -2.784798384.Subproblem 1
t + -2.857142857 = 2.784798384 Simplifying t + -2.857142857 = 2.784798384 Reorder the terms: -2.857142857 + t = 2.784798384 Solving -2.857142857 + t = 2.784798384 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = 2.784798384 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = 2.784798384 + 2.857142857 t = 2.784798384 + 2.857142857 Combine like terms: 2.784798384 + 2.857142857 = 5.641941241 t = 5.641941241 Simplifying t = 5.641941241Subproblem 2
t + -2.857142857 = -2.784798384 Simplifying t + -2.857142857 = -2.784798384 Reorder the terms: -2.857142857 + t = -2.784798384 Solving -2.857142857 + t = -2.784798384 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.857142857' to each side of the equation. -2.857142857 + 2.857142857 + t = -2.784798384 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = -2.784798384 + 2.857142857 t = -2.784798384 + 2.857142857 Combine like terms: -2.784798384 + 2.857142857 = 0.072344473 t = 0.072344473 Simplifying t = 0.072344473Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.641941241, 0.072344473}
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