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Simplifying 0 = -4.9t2 + 5t + 950 Reorder the terms: 0 = 950 + 5t + -4.9t2 Solving 0 = 950 + 5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -950 = -950 -950 + -5t + 4.9t2 = 950 + 5t + -4.9t2 + -950 + -5t + 4.9t2 Reorder the terms: -950 + -5t + 4.9t2 = 950 + -950 + 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 950 + -950 = 0 -950 + -5t + 4.9t2 = 0 + 5t + -5t + -4.9t2 + 4.9t2 -950 + -5t + 4.9t2 = 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 5t + -5t = 0 -950 + -5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -950 + -5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -950 + -5t + 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'. -193.877551 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '193.877551' to each side of the equation. -193.877551 + -1.020408163t + 193.877551 + t2 = 0 + 193.877551 Reorder the terms: -193.877551 + 193.877551 + -1.020408163t + t2 = 0 + 193.877551 Combine like terms: -193.877551 + 193.877551 = 0.000000 0.000000 + -1.020408163t + t2 = 0 + 193.877551 -1.020408163t + t2 = 0 + 193.877551 Combine like terms: 0 + 193.877551 = 193.877551 -1.020408163t + t2 = 193.877551 The t term is -1.020408163t. Take half its coefficient (-0.5102040815). Square it (0.2603082048) and add it to both sides. Add '0.2603082048' to each side of the equation. -1.020408163t + 0.2603082048 + t2 = 193.877551 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 193.877551 + 0.2603082048 Combine like terms: 193.877551 + 0.2603082048 = 194.1378592048 0.2603082048 + -1.020408163t + t2 = 194.1378592048 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 194.1378592048 Calculate the square root of the right side: 13.933336255 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 13.933336255 and -13.933336255.Subproblem 1
t + -0.5102040815 = 13.933336255 Simplifying t + -0.5102040815 = 13.933336255 Reorder the terms: -0.5102040815 + t = 13.933336255 Solving -0.5102040815 + t = 13.933336255 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = 13.933336255 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 13.933336255 + 0.5102040815 t = 13.933336255 + 0.5102040815 Combine like terms: 13.933336255 + 0.5102040815 = 14.4435403365 t = 14.4435403365 Simplifying t = 14.4435403365Subproblem 2
t + -0.5102040815 = -13.933336255 Simplifying t + -0.5102040815 = -13.933336255 Reorder the terms: -0.5102040815 + t = -13.933336255 Solving -0.5102040815 + t = -13.933336255 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5102040815' to each side of the equation. -0.5102040815 + 0.5102040815 + t = -13.933336255 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -13.933336255 + 0.5102040815 t = -13.933336255 + 0.5102040815 Combine like terms: -13.933336255 + 0.5102040815 = -13.4231321735 t = -13.4231321735 Simplifying t = -13.4231321735Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.4435403365, -13.4231321735}
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