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Simplifying -4.9t2 + -28t + 40 = 0 Reorder the terms: 40 + -28t + -4.9t2 = 0 Solving 40 + -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'. -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 = 1.183467321 t = 1.183467321 Simplifying t = 1.183467321Subproblem 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 = -6.897753035 t = -6.897753035 Simplifying t = -6.897753035Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.183467321, -6.897753035}
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