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Simplifying 4.9t2 + -28t + 30 = 0 Reorder the terms: 30 + -28t + 4.9t2 = 0 Solving 30 + -28t + 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'. 6.12244898 + -5.714285714t + t2 = 0 Move the constant term to the right: Add '-6.12244898' to each side of the equation. 6.12244898 + -5.714285714t + -6.12244898 + t2 = 0 + -6.12244898 Reorder the terms: 6.12244898 + -6.12244898 + -5.714285714t + t2 = 0 + -6.12244898 Combine like terms: 6.12244898 + -6.12244898 = 0.00000000 0.00000000 + -5.714285714t + t2 = 0 + -6.12244898 -5.714285714t + t2 = 0 + -6.12244898 Combine like terms: 0 + -6.12244898 = -6.12244898 -5.714285714t + t2 = -6.12244898 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 = -6.12244898 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714t + t2 = -6.12244898 + 8.163265305 Combine like terms: -6.12244898 + 8.163265305 = 2.040816325 8.163265305 + -5.714285714t + t2 = 2.040816325 Factor a perfect square on the left side: (t + -2.857142857)(t + -2.857142857) = 2.040816325 Calculate the square root of the right side: 1.428571428 Break this problem into two subproblems by setting (t + -2.857142857) equal to 1.428571428 and -1.428571428.Subproblem 1
t + -2.857142857 = 1.428571428 Simplifying t + -2.857142857 = 1.428571428 Reorder the terms: -2.857142857 + t = 1.428571428 Solving -2.857142857 + t = 1.428571428 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 = 1.428571428 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = 1.428571428 + 2.857142857 t = 1.428571428 + 2.857142857 Combine like terms: 1.428571428 + 2.857142857 = 4.285714285 t = 4.285714285 Simplifying t = 4.285714285Subproblem 2
t + -2.857142857 = -1.428571428 Simplifying t + -2.857142857 = -1.428571428 Reorder the terms: -2.857142857 + t = -1.428571428 Solving -2.857142857 + t = -1.428571428 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 = -1.428571428 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = -1.428571428 + 2.857142857 t = -1.428571428 + 2.857142857 Combine like terms: -1.428571428 + 2.857142857 = 1.428571429 t = 1.428571429 Simplifying t = 1.428571429Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.285714285, 1.428571429}
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