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Simplifying -2.2 = 4.9t2 + 9.9t Reorder the terms: -2.2 = 9.9t + 4.9t2 Solving -2.2 = 9.9t + 4.9t2 Solving for variable 't'. Reorder the terms: -2.2 + -9.9t + -4.9t2 = 9.9t + -9.9t + 4.9t2 + -4.9t2 Combine like terms: 9.9t + -9.9t = 0.0 -2.2 + -9.9t + -4.9t2 = 0.0 + 4.9t2 + -4.9t2 -2.2 + -9.9t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 -2.2 + -9.9t + -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'. 0.4489795918 + 2.020408163t + t2 = 0 Move the constant term to the right: Add '-0.4489795918' to each side of the equation. 0.4489795918 + 2.020408163t + -0.4489795918 + t2 = 0 + -0.4489795918 Reorder the terms: 0.4489795918 + -0.4489795918 + 2.020408163t + t2 = 0 + -0.4489795918 Combine like terms: 0.4489795918 + -0.4489795918 = 0.0000000000 0.0000000000 + 2.020408163t + t2 = 0 + -0.4489795918 2.020408163t + t2 = 0 + -0.4489795918 Combine like terms: 0 + -0.4489795918 = -0.4489795918 2.020408163t + t2 = -0.4489795918 The t term is 2.020408163t. Take half its coefficient (1.010204082). Square it (1.020512287) and add it to both sides. Add '1.020512287' to each side of the equation. 2.020408163t + 1.020512287 + t2 = -0.4489795918 + 1.020512287 Reorder the terms: 1.020512287 + 2.020408163t + t2 = -0.4489795918 + 1.020512287 Combine like terms: -0.4489795918 + 1.020512287 = 0.5715326952 1.020512287 + 2.020408163t + t2 = 0.5715326952 Factor a perfect square on the left side: (t + 1.010204082)(t + 1.010204082) = 0.5715326952 Calculate the square root of the right side: 0.755997814 Break this problem into two subproblems by setting (t + 1.010204082) equal to 0.755997814 and -0.755997814.Subproblem 1
t + 1.010204082 = 0.755997814 Simplifying t + 1.010204082 = 0.755997814 Reorder the terms: 1.010204082 + t = 0.755997814 Solving 1.010204082 + t = 0.755997814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.010204082' to each side of the equation. 1.010204082 + -1.010204082 + t = 0.755997814 + -1.010204082 Combine like terms: 1.010204082 + -1.010204082 = 0.000000000 0.000000000 + t = 0.755997814 + -1.010204082 t = 0.755997814 + -1.010204082 Combine like terms: 0.755997814 + -1.010204082 = -0.254206268 t = -0.254206268 Simplifying t = -0.254206268Subproblem 2
t + 1.010204082 = -0.755997814 Simplifying t + 1.010204082 = -0.755997814 Reorder the terms: 1.010204082 + t = -0.755997814 Solving 1.010204082 + t = -0.755997814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.010204082' to each side of the equation. 1.010204082 + -1.010204082 + t = -0.755997814 + -1.010204082 Combine like terms: 1.010204082 + -1.010204082 = 0.000000000 0.000000000 + t = -0.755997814 + -1.010204082 t = -0.755997814 + -1.010204082 Combine like terms: -0.755997814 + -1.010204082 = -1.766201896 t = -1.766201896 Simplifying t = -1.766201896Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.254206268, -1.766201896}
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