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Simplifying 4.9t * t + -5t = 300 Multiply t * t 4.9t2 + -5t = 300 Reorder the terms: -5t + 4.9t2 = 300 Solving -5t + 4.9t2 = 300 Solving for variable 't'. Reorder the terms: -300 + -5t + 4.9t2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + -5t + 4.9t2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -61.2244898 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '61.2244898' to each side of the equation. -61.2244898 + -1.020408163t + 61.2244898 + t2 = 0 + 61.2244898 Reorder the terms: -61.2244898 + 61.2244898 + -1.020408163t + t2 = 0 + 61.2244898 Combine like terms: -61.2244898 + 61.2244898 = 0.0000000 0.0000000 + -1.020408163t + t2 = 0 + 61.2244898 -1.020408163t + t2 = 0 + 61.2244898 Combine like terms: 0 + 61.2244898 = 61.2244898 -1.020408163t + t2 = 61.2244898 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 = 61.2244898 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 61.2244898 + 0.2603082048 Combine like terms: 61.2244898 + 0.2603082048 = 61.4847980048 0.2603082048 + -1.020408163t + t2 = 61.4847980048 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 61.4847980048 Calculate the square root of the right side: 7.841224267 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 7.841224267 and -7.841224267.Subproblem 1
t + -0.5102040815 = 7.841224267 Simplifying t + -0.5102040815 = 7.841224267 Reorder the terms: -0.5102040815 + t = 7.841224267 Solving -0.5102040815 + t = 7.841224267 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 = 7.841224267 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 7.841224267 + 0.5102040815 t = 7.841224267 + 0.5102040815 Combine like terms: 7.841224267 + 0.5102040815 = 8.3514283485 t = 8.3514283485 Simplifying t = 8.3514283485Subproblem 2
t + -0.5102040815 = -7.841224267 Simplifying t + -0.5102040815 = -7.841224267 Reorder the terms: -0.5102040815 + t = -7.841224267 Solving -0.5102040815 + t = -7.841224267 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 = -7.841224267 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -7.841224267 + 0.5102040815 t = -7.841224267 + 0.5102040815 Combine like terms: -7.841224267 + 0.5102040815 = -7.3310201855 t = -7.3310201855 Simplifying t = -7.3310201855Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.3514283485, -7.3310201855}
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