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Simplifying -4.9t2 + 50t + -35 = 0 Reorder the terms: -35 + 50t + -4.9t2 = 0 Solving -35 + 50t + -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'. 7.142857143 + -10.20408163t + t2 = 0 Move the constant term to the right: Add '-7.142857143' to each side of the equation. 7.142857143 + -10.20408163t + -7.142857143 + t2 = 0 + -7.142857143 Reorder the terms: 7.142857143 + -7.142857143 + -10.20408163t + t2 = 0 + -7.142857143 Combine like terms: 7.142857143 + -7.142857143 = 0.000000000 0.000000000 + -10.20408163t + t2 = 0 + -7.142857143 -10.20408163t + t2 = 0 + -7.142857143 Combine like terms: 0 + -7.142857143 = -7.142857143 -10.20408163t + t2 = -7.142857143 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 = -7.142857143 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163t + t2 = -7.142857143 + 26.03082048 Combine like terms: -7.142857143 + 26.03082048 = 18.887963337 26.03082048 + -10.20408163t + t2 = 18.887963337 Factor a perfect square on the left side: (t + -5.102040815)(t + -5.102040815) = 18.887963337 Calculate the square root of the right side: 4.346028456 Break this problem into two subproblems by setting (t + -5.102040815) equal to 4.346028456 and -4.346028456.Subproblem 1
t + -5.102040815 = 4.346028456 Simplifying t + -5.102040815 = 4.346028456 Reorder the terms: -5.102040815 + t = 4.346028456 Solving -5.102040815 + t = 4.346028456 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 = 4.346028456 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + t = 4.346028456 + 5.102040815 t = 4.346028456 + 5.102040815 Combine like terms: 4.346028456 + 5.102040815 = 9.448069271 t = 9.448069271 Simplifying t = 9.448069271Subproblem 2
t + -5.102040815 = -4.346028456 Simplifying t + -5.102040815 = -4.346028456 Reorder the terms: -5.102040815 + t = -4.346028456 Solving -5.102040815 + t = -4.346028456 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 = -4.346028456 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + t = -4.346028456 + 5.102040815 t = -4.346028456 + 5.102040815 Combine like terms: -4.346028456 + 5.102040815 = 0.756012359 t = 0.756012359 Simplifying t = 0.756012359Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.448069271, 0.756012359}
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