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Simplifying (-4.9t2) + (3t) + 550 = 0 Reorder the terms: 550 + (3t) + (-4.9t2) = 0 Solving 550 + (3t) + (-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'. -112.244898 + (-0.612244898t) + t2 = 0 Move the constant term to the right: Add '112.244898' to each side of the equation. -112.244898 + (-0.612244898t) + 112.244898 + t2 = 0 + 112.244898 Reorder the terms: -112.244898 + 112.244898 + (-0.612244898t) + t2 = 0 + 112.244898 Combine like terms: -112.244898 + 112.244898 = 0.000000 0.000000 + (-0.612244898t) + t2 = 0 + 112.244898 (-0.612244898t) + t2 = 0 + 112.244898 Combine like terms: 0 + 112.244898 = 112.244898 (-0.612244898t) + t2 = 112.244898 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 = 112.244898 + 0.09371095378 Reorder the terms: 0.09371095378 + (-0.612244898t) + t2 = 112.244898 + 0.09371095378 Combine like terms: 112.244898 + 0.09371095378 = 112.33860895378 0.09371095378 + (-0.612244898t) + t2 = 112.33860895378 Factor a perfect square on the left side: ((t) + -0.306122449)((t) + -0.306122449) = 112.33860895378 Calculate the square root of the right side: 10.59899094 Break this problem into two subproblems by setting ((t) + -0.306122449) equal to 10.59899094 and -10.59899094.Subproblem 1
(t) + -0.306122449 = 10.59899094 Simplifying (t) + -0.306122449 = 10.59899094 t + -0.306122449 = 10.59899094 Reorder the terms: -0.306122449 + t = 10.59899094 Solving -0.306122449 + t = 10.59899094 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 = 10.59899094 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = 10.59899094 + 0.306122449 t = 10.59899094 + 0.306122449 Combine like terms: 10.59899094 + 0.306122449 = 10.905113389 t = 10.905113389 Simplifying t = 10.905113389Subproblem 2
(t) + -0.306122449 = -10.59899094 Simplifying (t) + -0.306122449 = -10.59899094 t + -0.306122449 = -10.59899094 Reorder the terms: -0.306122449 + t = -10.59899094 Solving -0.306122449 + t = -10.59899094 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 = -10.59899094 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = -10.59899094 + 0.306122449 t = -10.59899094 + 0.306122449 Combine like terms: -10.59899094 + 0.306122449 = -10.292868491 t = -10.292868491 Simplifying t = -10.292868491Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.905113389, -10.292868491}
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