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Simplifying -38 = 2 + 28t + -4.9t2 Solving -38 = 2 + 28t + -4.9t2 Solving for variable 't'. Combine like terms: -38 + -2 = -40 -40 + -28t + 4.9t2 = 2 + 28t + -4.9t2 + -2 + -28t + 4.9t2 Reorder the terms: -40 + -28t + 4.9t2 = 2 + -2 + 28t + -28t + -4.9t2 + 4.9t2 Combine like terms: 2 + -2 = 0 -40 + -28t + 4.9t2 = 0 + 28t + -28t + -4.9t2 + 4.9t2 -40 + -28t + 4.9t2 = 28t + -28t + -4.9t2 + 4.9t2 Combine like terms: 28t + -28t = 0 -40 + -28t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -40 + -28t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -40 + -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'. -8.163265306 + -5.714285714t + t2 = 0 Move the constant term to the right: Add '8.163265306' to each side of the equation. -8.163265306 + -5.714285714t + 8.163265306 + t2 = 0 + 8.163265306 Reorder the terms: -8.163265306 + 8.163265306 + -5.714285714t + t2 = 0 + 8.163265306 Combine like terms: -8.163265306 + 8.163265306 = 0.000000000 0.000000000 + -5.714285714t + t2 = 0 + 8.163265306 -5.714285714t + t2 = 0 + 8.163265306 Combine like terms: 0 + 8.163265306 = 8.163265306 -5.714285714t + t2 = 8.163265306 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 = 8.163265306 + 8.163265305 Reorder the terms: 8.163265305 + -5.714285714t + t2 = 8.163265306 + 8.163265305 Combine like terms: 8.163265306 + 8.163265305 = 16.326530611 8.163265305 + -5.714285714t + t2 = 16.326530611 Factor a perfect square on the left side: (t + -2.857142857)(t + -2.857142857) = 16.326530611 Calculate the square root of the right side: 4.040610178 Break this problem into two subproblems by setting (t + -2.857142857) equal to 4.040610178 and -4.040610178.Subproblem 1
t + -2.857142857 = 4.040610178 Simplifying t + -2.857142857 = 4.040610178 Reorder the terms: -2.857142857 + t = 4.040610178 Solving -2.857142857 + t = 4.040610178 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 = 4.040610178 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = 4.040610178 + 2.857142857 t = 4.040610178 + 2.857142857 Combine like terms: 4.040610178 + 2.857142857 = 6.897753035 t = 6.897753035 Simplifying t = 6.897753035Subproblem 2
t + -2.857142857 = -4.040610178 Simplifying t + -2.857142857 = -4.040610178 Reorder the terms: -2.857142857 + t = -4.040610178 Solving -2.857142857 + t = -4.040610178 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 = -4.040610178 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + t = -4.040610178 + 2.857142857 t = -4.040610178 + 2.857142857 Combine like terms: -4.040610178 + 2.857142857 = -1.183467321 t = -1.183467321 Simplifying t = -1.183467321Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.897753035, -1.183467321}
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