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Simplifying 0 = -4.9t2 + 50t + 5 Reorder the terms: 0 = 5 + 50t + -4.9t2 Solving 0 = 5 + 50t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -50t + 4.9t2 = 5 + 50t + -4.9t2 + -5 + -50t + 4.9t2 Reorder the terms: -5 + -50t + 4.9t2 = 5 + -5 + 50t + -50t + -4.9t2 + 4.9t2 Combine like terms: 5 + -5 = 0 -5 + -50t + 4.9t2 = 0 + 50t + -50t + -4.9t2 + 4.9t2 -5 + -50t + 4.9t2 = 50t + -50t + -4.9t2 + 4.9t2 Combine like terms: 50t + -50t = 0 -5 + -50t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -5 + -50t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -5 + -50t + 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'. -1.020408163 + -10.20408163t + t2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -10.20408163t + 1.020408163 + t2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -10.20408163t + t2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -10.20408163t + t2 = 0 + 1.020408163 -10.20408163t + t2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -10.20408163t + t2 = 1.020408163 The t term is -10.20408163t. Take half its coefficient (-5.102040815). Square it (26.03082048) and add it to both sides. Add '26.03082048' to each side of the equation. -10.20408163t + 26.03082048 + t2 = 1.020408163 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163t + t2 = 1.020408163 + 26.03082048 Combine like terms: 1.020408163 + 26.03082048 = 27.051228643 26.03082048 + -10.20408163t + t2 = 27.051228643 Factor a perfect square on the left side: (t + -5.102040815)(t + -5.102040815) = 27.051228643 Calculate the square root of the right side: 5.201079565 Break this problem into two subproblems by setting (t + -5.102040815) equal to 5.201079565 and -5.201079565.Subproblem 1
t + -5.102040815 = 5.201079565 Simplifying t + -5.102040815 = 5.201079565 Reorder the terms: -5.102040815 + t = 5.201079565 Solving -5.102040815 + t = 5.201079565 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + t = 5.201079565 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + t = 5.201079565 + 5.102040815 t = 5.201079565 + 5.102040815 Combine like terms: 5.201079565 + 5.102040815 = 10.30312038 t = 10.30312038 Simplifying t = 10.30312038Subproblem 2
t + -5.102040815 = -5.201079565 Simplifying t + -5.102040815 = -5.201079565 Reorder the terms: -5.102040815 + t = -5.201079565 Solving -5.102040815 + t = -5.201079565 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + t = -5.201079565 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + t = -5.201079565 + 5.102040815 t = -5.201079565 + 5.102040815 Combine like terms: -5.201079565 + 5.102040815 = -0.09903875 t = -0.09903875 Simplifying t = -0.09903875Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.30312038, -0.09903875}
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