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Simplifying 53.1 = 3t + 4.9t2 Solving 53.1 = 3t + 4.9t2 Solving for variable 't'. Reorder the terms: 53.1 + -3t + -4.9t2 = 3t + -3t + 4.9t2 + -4.9t2 Combine like terms: 3t + -3t = 0 53.1 + -3t + -4.9t2 = 0 + 4.9t2 + -4.9t2 53.1 + -3t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 53.1 + -3t + -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'. -10.83673469 + 0.612244898t + t2 = 0 Move the constant term to the right: Add '10.83673469' to each side of the equation. -10.83673469 + 0.612244898t + 10.83673469 + t2 = 0 + 10.83673469 Reorder the terms: -10.83673469 + 10.83673469 + 0.612244898t + t2 = 0 + 10.83673469 Combine like terms: -10.83673469 + 10.83673469 = 0.00000000 0.00000000 + 0.612244898t + t2 = 0 + 10.83673469 0.612244898t + t2 = 0 + 10.83673469 Combine like terms: 0 + 10.83673469 = 10.83673469 0.612244898t + t2 = 10.83673469 The t term is 0.612244898t. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898t + 0.09371095378 + t2 = 10.83673469 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898t + t2 = 10.83673469 + 0.09371095378 Combine like terms: 10.83673469 + 0.09371095378 = 10.93044564378 0.09371095378 + 0.612244898t + t2 = 10.93044564378 Factor a perfect square on the left side: (t + 0.306122449)(t + 0.306122449) = 10.93044564378 Calculate the square root of the right side: 3.306122448 Break this problem into two subproblems by setting (t + 0.306122449) equal to 3.306122448 and -3.306122448.Subproblem 1
t + 0.306122449 = 3.306122448 Simplifying t + 0.306122449 = 3.306122448 Reorder the terms: 0.306122449 + t = 3.306122448 Solving 0.306122449 + t = 3.306122448 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = 3.306122448 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = 3.306122448 + -0.306122449 t = 3.306122448 + -0.306122449 Combine like terms: 3.306122448 + -0.306122449 = 2.999999999 t = 2.999999999 Simplifying t = 2.999999999Subproblem 2
t + 0.306122449 = -3.306122448 Simplifying t + 0.306122449 = -3.306122448 Reorder the terms: 0.306122449 + t = -3.306122448 Solving 0.306122449 + t = -3.306122448 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + t = -3.306122448 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + t = -3.306122448 + -0.306122449 t = -3.306122448 + -0.306122449 Combine like terms: -3.306122448 + -0.306122449 = -3.612244897 t = -3.612244897 Simplifying t = -3.612244897Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.999999999, -3.612244897}
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