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Simplifying 500 + 14t + -4.9t2 = 0 Solving 500 + 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'. -102.0408163 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + -2.857142857t + 102.0408163 + t2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + -2.857142857t + t2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + -2.857142857t + t2 = 0 + 102.0408163 -2.857142857t + t2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 -2.857142857t + t2 = 102.0408163 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 = 102.0408163 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = 102.0408163 + 2.040816328 Combine like terms: 102.0408163 + 2.040816328 = 104.081632628 2.040816328 + -2.857142857t + t2 = 104.081632628 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 104.081632628 Calculate the square root of the right side: 10.202040611 Break this problem into two subproblems by setting (t + -1.428571429) equal to 10.202040611 and -10.202040611.Subproblem 1
t + -1.428571429 = 10.202040611 Simplifying t + -1.428571429 = 10.202040611 Reorder the terms: -1.428571429 + t = 10.202040611 Solving -1.428571429 + t = 10.202040611 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 = 10.202040611 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 10.202040611 + 1.428571429 t = 10.202040611 + 1.428571429 Combine like terms: 10.202040611 + 1.428571429 = 11.63061204 t = 11.63061204 Simplifying t = 11.63061204Subproblem 2
t + -1.428571429 = -10.202040611 Simplifying t + -1.428571429 = -10.202040611 Reorder the terms: -1.428571429 + t = -10.202040611 Solving -1.428571429 + t = -10.202040611 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 = -10.202040611 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -10.202040611 + 1.428571429 t = -10.202040611 + 1.428571429 Combine like terms: -10.202040611 + 1.428571429 = -8.773469182 t = -8.773469182 Simplifying t = -8.773469182Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.63061204, -8.773469182}
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