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Simplifying t = -4.9t2 + 3.5t + 10 Reorder the terms: t = 10 + 3.5t + -4.9t2 Solving t = 10 + 3.5t + -4.9t2 Solving for variable 't'. Reorder the terms: -10 + t + -3.5t + 4.9t2 = 10 + 3.5t + -4.9t2 + -10 + -3.5t + 4.9t2 Combine like terms: t + -3.5t = -2.5t -10 + -2.5t + 4.9t2 = 10 + 3.5t + -4.9t2 + -10 + -3.5t + 4.9t2 Reorder the terms: -10 + -2.5t + 4.9t2 = 10 + -10 + 3.5t + -3.5t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -10 + -2.5t + 4.9t2 = 0 + 3.5t + -3.5t + -4.9t2 + 4.9t2 -10 + -2.5t + 4.9t2 = 3.5t + -3.5t + -4.9t2 + 4.9t2 Combine like terms: 3.5t + -3.5t = 0.0 -10 + -2.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -10 + -2.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + -2.5t + 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'. -2.040816327 + -0.5102040816t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -0.5102040816t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -0.5102040816t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -0.5102040816t + t2 = 0 + 2.040816327 -0.5102040816t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -0.5102040816t + t2 = 2.040816327 The t term is -0.5102040816t. Take half its coefficient (-0.2551020408). Square it (0.06507705122) and add it to both sides. Add '0.06507705122' to each side of the equation. -0.5102040816t + 0.06507705122 + t2 = 2.040816327 + 0.06507705122 Reorder the terms: 0.06507705122 + -0.5102040816t + t2 = 2.040816327 + 0.06507705122 Combine like terms: 2.040816327 + 0.06507705122 = 2.10589337822 0.06507705122 + -0.5102040816t + t2 = 2.10589337822 Factor a perfect square on the left side: (t + -0.2551020408)(t + -0.2551020408) = 2.10589337822 Calculate the square root of the right side: 1.451169659 Break this problem into two subproblems by setting (t + -0.2551020408) equal to 1.451169659 and -1.451169659.Subproblem 1
t + -0.2551020408 = 1.451169659 Simplifying t + -0.2551020408 = 1.451169659 Reorder the terms: -0.2551020408 + t = 1.451169659 Solving -0.2551020408 + t = 1.451169659 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = 1.451169659 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = 1.451169659 + 0.2551020408 t = 1.451169659 + 0.2551020408 Combine like terms: 1.451169659 + 0.2551020408 = 1.7062716998 t = 1.7062716998 Simplifying t = 1.7062716998Subproblem 2
t + -0.2551020408 = -1.451169659 Simplifying t + -0.2551020408 = -1.451169659 Reorder the terms: -0.2551020408 + t = -1.451169659 Solving -0.2551020408 + t = -1.451169659 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2551020408' to each side of the equation. -0.2551020408 + 0.2551020408 + t = -1.451169659 + 0.2551020408 Combine like terms: -0.2551020408 + 0.2551020408 = 0.0000000000 0.0000000000 + t = -1.451169659 + 0.2551020408 t = -1.451169659 + 0.2551020408 Combine like terms: -1.451169659 + 0.2551020408 = -1.1960676182 t = -1.1960676182 Simplifying t = -1.1960676182Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.7062716998, -1.1960676182}
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