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Simplifying -4.9t2 + 14t + 100 = 0 Reorder the terms: 100 + 14t + -4.9t2 = 0 Solving 100 + 14t + -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'. -20.40816327 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '20.40816327' to each side of the equation. -20.40816327 + -2.857142857t + 20.40816327 + t2 = 0 + 20.40816327 Reorder the terms: -20.40816327 + 20.40816327 + -2.857142857t + t2 = 0 + 20.40816327 Combine like terms: -20.40816327 + 20.40816327 = 0.00000000 0.00000000 + -2.857142857t + t2 = 0 + 20.40816327 -2.857142857t + t2 = 0 + 20.40816327 Combine like terms: 0 + 20.40816327 = 20.40816327 -2.857142857t + t2 = 20.40816327 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = 20.40816327 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 20.40816327 + 2.040816328 Combine like terms: 20.40816327 + 2.040816328 = 22.448979598 2.040816328 + -2.857142857t + t2 = 22.448979598 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 22.448979598 Calculate the square root of the right side: 4.738035415 Break this problem into two subproblems by setting (t + -1.428571429) equal to 4.738035415 and -4.738035415.Subproblem 1
t + -1.428571429 = 4.738035415 Simplifying t + -1.428571429 = 4.738035415 Reorder the terms: -1.428571429 + t = 4.738035415 Solving -1.428571429 + t = 4.738035415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 4.738035415 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 4.738035415 + 1.428571429 t = 4.738035415 + 1.428571429 Combine like terms: 4.738035415 + 1.428571429 = 6.166606844 t = 6.166606844 Simplifying t = 6.166606844Subproblem 2
t + -1.428571429 = -4.738035415 Simplifying t + -1.428571429 = -4.738035415 Reorder the terms: -1.428571429 + t = -4.738035415 Solving -1.428571429 + t = -4.738035415 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -4.738035415 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -4.738035415 + 1.428571429 t = -4.738035415 + 1.428571429 Combine like terms: -4.738035415 + 1.428571429 = -3.309463986 t = -3.309463986 Simplifying t = -3.309463986Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.166606844, -3.309463986}
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