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Simplifying 1190 + 105.2t + -4.9t2 = 0 Solving 1190 + 105.2t + -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'. -242.8571429 + -21.46938776t + t2 = 0 Move the constant term to the right: Add '242.8571429' to each side of the equation. -242.8571429 + -21.46938776t + 242.8571429 + t2 = 0 + 242.8571429 Reorder the terms: -242.8571429 + 242.8571429 + -21.46938776t + t2 = 0 + 242.8571429 Combine like terms: -242.8571429 + 242.8571429 = 0.0000000 0.0000000 + -21.46938776t + t2 = 0 + 242.8571429 -21.46938776t + t2 = 0 + 242.8571429 Combine like terms: 0 + 242.8571429 = 242.8571429 -21.46938776t + t2 = 242.8571429 The t term is -21.46938776t. Take half its coefficient (-10.73469388). Square it (115.2336527) and add it to both sides. Add '115.2336527' to each side of the equation. -21.46938776t + 115.2336527 + t2 = 242.8571429 + 115.2336527 Reorder the terms: 115.2336527 + -21.46938776t + t2 = 242.8571429 + 115.2336527 Combine like terms: 242.8571429 + 115.2336527 = 358.0907956 115.2336527 + -21.46938776t + t2 = 358.0907956 Factor a perfect square on the left side: (t + -10.73469388)(t + -10.73469388) = 358.0907956 Calculate the square root of the right side: 18.923287125 Break this problem into two subproblems by setting (t + -10.73469388) equal to 18.923287125 and -18.923287125.Subproblem 1
t + -10.73469388 = 18.923287125 Simplifying t + -10.73469388 = 18.923287125 Reorder the terms: -10.73469388 + t = 18.923287125 Solving -10.73469388 + t = 18.923287125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.73469388' to each side of the equation. -10.73469388 + 10.73469388 + t = 18.923287125 + 10.73469388 Combine like terms: -10.73469388 + 10.73469388 = 0.00000000 0.00000000 + t = 18.923287125 + 10.73469388 t = 18.923287125 + 10.73469388 Combine like terms: 18.923287125 + 10.73469388 = 29.657981005 t = 29.657981005 Simplifying t = 29.657981005Subproblem 2
t + -10.73469388 = -18.923287125 Simplifying t + -10.73469388 = -18.923287125 Reorder the terms: -10.73469388 + t = -18.923287125 Solving -10.73469388 + t = -18.923287125 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10.73469388' to each side of the equation. -10.73469388 + 10.73469388 + t = -18.923287125 + 10.73469388 Combine like terms: -10.73469388 + 10.73469388 = 0.00000000 0.00000000 + t = -18.923287125 + 10.73469388 t = -18.923287125 + 10.73469388 Combine like terms: -18.923287125 + 10.73469388 = -8.188593245 t = -8.188593245 Simplifying t = -8.188593245Solution
The solution to the problem is based on the solutions from the subproblems. t = {29.657981005, -8.188593245}
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