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Simplifying 0 = -4.9t2 + 5t + 9 Reorder the terms: 0 = 9 + 5t + -4.9t2 Solving 0 = 9 + 5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -9 = -9 -9 + -5t + 4.9t2 = 9 + 5t + -4.9t2 + -9 + -5t + 4.9t2 Reorder the terms: -9 + -5t + 4.9t2 = 9 + -9 + 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 9 + -9 = 0 -9 + -5t + 4.9t2 = 0 + 5t + -5t + -4.9t2 + 4.9t2 -9 + -5t + 4.9t2 = 5t + -5t + -4.9t2 + 4.9t2 Combine like terms: 5t + -5t = 0 -9 + -5t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -9 + -5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -9 + -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'. -1.836734694 + -1.020408163t + t2 = 0 Move the constant term to the right: Add '1.836734694' to each side of the equation. -1.836734694 + -1.020408163t + 1.836734694 + t2 = 0 + 1.836734694 Reorder the terms: -1.836734694 + 1.836734694 + -1.020408163t + t2 = 0 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + -1.020408163t + t2 = 0 + 1.836734694 -1.020408163t + t2 = 0 + 1.836734694 Combine like terms: 0 + 1.836734694 = 1.836734694 -1.020408163t + t2 = 1.836734694 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 = 1.836734694 + 0.2603082048 Reorder the terms: 0.2603082048 + -1.020408163t + t2 = 1.836734694 + 0.2603082048 Combine like terms: 1.836734694 + 0.2603082048 = 2.0970428988 0.2603082048 + -1.020408163t + t2 = 2.0970428988 Factor a perfect square on the left side: (t + -0.5102040815)(t + -0.5102040815) = 2.0970428988 Calculate the square root of the right side: 1.448117018 Break this problem into two subproblems by setting (t + -0.5102040815) equal to 1.448117018 and -1.448117018.Subproblem 1
t + -0.5102040815 = 1.448117018 Simplifying t + -0.5102040815 = 1.448117018 Reorder the terms: -0.5102040815 + t = 1.448117018 Solving -0.5102040815 + t = 1.448117018 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 = 1.448117018 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = 1.448117018 + 0.5102040815 t = 1.448117018 + 0.5102040815 Combine like terms: 1.448117018 + 0.5102040815 = 1.9583210995 t = 1.9583210995 Simplifying t = 1.9583210995Subproblem 2
t + -0.5102040815 = -1.448117018 Simplifying t + -0.5102040815 = -1.448117018 Reorder the terms: -0.5102040815 + t = -1.448117018 Solving -0.5102040815 + t = -1.448117018 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 = -1.448117018 + 0.5102040815 Combine like terms: -0.5102040815 + 0.5102040815 = 0.0000000000 0.0000000000 + t = -1.448117018 + 0.5102040815 t = -1.448117018 + 0.5102040815 Combine like terms: -1.448117018 + 0.5102040815 = -0.9379129365 t = -0.9379129365 Simplifying t = -0.9379129365Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.9583210995, -0.9379129365}
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