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Simplifying -3 = 10.38t + -4.9t2 Solving -3 = 10.38t + -4.9t2 Solving for variable 't'. Reorder the terms: -3 + -10.38t + 4.9t2 = 10.38t + -10.38t + -4.9t2 + 4.9t2 Combine like terms: 10.38t + -10.38t = 0.00 -3 + -10.38t + 4.9t2 = 0.00 + -4.9t2 + 4.9t2 -3 + -10.38t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -3 + -10.38t + 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'. -0.612244898 + -2.118367347t + t2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -2.118367347t + 0.612244898 + t2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -2.118367347t + t2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -2.118367347t + t2 = 0 + 0.612244898 -2.118367347t + t2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -2.118367347t + t2 = 0.612244898 The t term is -2.118367347t. Take half its coefficient (-1.059183674). Square it (1.121870055) and add it to both sides. Add '1.121870055' to each side of the equation. -2.118367347t + 1.121870055 + t2 = 0.612244898 + 1.121870055 Reorder the terms: 1.121870055 + -2.118367347t + t2 = 0.612244898 + 1.121870055 Combine like terms: 0.612244898 + 1.121870055 = 1.734114953 1.121870055 + -2.118367347t + t2 = 1.734114953 Factor a perfect square on the left side: (t + -1.059183674)(t + -1.059183674) = 1.734114953 Calculate the square root of the right side: 1.316857985 Break this problem into two subproblems by setting (t + -1.059183674) equal to 1.316857985 and -1.316857985.Subproblem 1
t + -1.059183674 = 1.316857985 Simplifying t + -1.059183674 = 1.316857985 Reorder the terms: -1.059183674 + t = 1.316857985 Solving -1.059183674 + t = 1.316857985 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.059183674' to each side of the equation. -1.059183674 + 1.059183674 + t = 1.316857985 + 1.059183674 Combine like terms: -1.059183674 + 1.059183674 = 0.000000000 0.000000000 + t = 1.316857985 + 1.059183674 t = 1.316857985 + 1.059183674 Combine like terms: 1.316857985 + 1.059183674 = 2.376041659 t = 2.376041659 Simplifying t = 2.376041659Subproblem 2
t + -1.059183674 = -1.316857985 Simplifying t + -1.059183674 = -1.316857985 Reorder the terms: -1.059183674 + t = -1.316857985 Solving -1.059183674 + t = -1.316857985 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.059183674' to each side of the equation. -1.059183674 + 1.059183674 + t = -1.316857985 + 1.059183674 Combine like terms: -1.059183674 + 1.059183674 = 0.000000000 0.000000000 + t = -1.316857985 + 1.059183674 t = -1.316857985 + 1.059183674 Combine like terms: -1.316857985 + 1.059183674 = -0.257674311 t = -0.257674311 Simplifying t = -0.257674311Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.376041659, -0.257674311}
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