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Simplifying -0.25 = 3.112t + -1(4.9) * t2 Multiply -1 * 4.9 -0.25 = 3.112t + -4.9t2 Solving -0.25 = 3.112t + -4.9t2 Solving for variable 't'. Reorder the terms: -0.25 + -3.112t + 4.9t2 = 3.112t + -3.112t + -4.9t2 + 4.9t2 Combine like terms: 3.112t + -3.112t = 0.000 -0.25 + -3.112t + 4.9t2 = 0.000 + -4.9t2 + 4.9t2 -0.25 + -3.112t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -0.25 + -3.112t + 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'. -0.05102040816 + -0.6351020408t + t2 = 0 Move the constant term to the right: Add '0.05102040816' to each side of the equation. -0.05102040816 + -0.6351020408t + 0.05102040816 + t2 = 0 + 0.05102040816 Reorder the terms: -0.05102040816 + 0.05102040816 + -0.6351020408t + t2 = 0 + 0.05102040816 Combine like terms: -0.05102040816 + 0.05102040816 = 0.00000000000 0.00000000000 + -0.6351020408t + t2 = 0 + 0.05102040816 -0.6351020408t + t2 = 0 + 0.05102040816 Combine like terms: 0 + 0.05102040816 = 0.05102040816 -0.6351020408t + t2 = 0.05102040816 The t term is -0.6351020408t. Take half its coefficient (-0.3175510204). Square it (0.1008386506) and add it to both sides. Add '0.1008386506' to each side of the equation. -0.6351020408t + 0.1008386506 + t2 = 0.05102040816 + 0.1008386506 Reorder the terms: 0.1008386506 + -0.6351020408t + t2 = 0.05102040816 + 0.1008386506 Combine like terms: 0.05102040816 + 0.1008386506 = 0.15185905876 0.1008386506 + -0.6351020408t + t2 = 0.15185905876 Factor a perfect square on the left side: (t + -0.3175510204)(t + -0.3175510204) = 0.15185905876 Calculate the square root of the right side: 0.389690979 Break this problem into two subproblems by setting (t + -0.3175510204) equal to 0.389690979 and -0.389690979.Subproblem 1
t + -0.3175510204 = 0.389690979 Simplifying t + -0.3175510204 = 0.389690979 Reorder the terms: -0.3175510204 + t = 0.389690979 Solving -0.3175510204 + t = 0.389690979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3175510204' to each side of the equation. -0.3175510204 + 0.3175510204 + t = 0.389690979 + 0.3175510204 Combine like terms: -0.3175510204 + 0.3175510204 = 0.0000000000 0.0000000000 + t = 0.389690979 + 0.3175510204 t = 0.389690979 + 0.3175510204 Combine like terms: 0.389690979 + 0.3175510204 = 0.7072419994 t = 0.7072419994 Simplifying t = 0.7072419994Subproblem 2
t + -0.3175510204 = -0.389690979 Simplifying t + -0.3175510204 = -0.389690979 Reorder the terms: -0.3175510204 + t = -0.389690979 Solving -0.3175510204 + t = -0.389690979 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3175510204' to each side of the equation. -0.3175510204 + 0.3175510204 + t = -0.389690979 + 0.3175510204 Combine like terms: -0.3175510204 + 0.3175510204 = 0.0000000000 0.0000000000 + t = -0.389690979 + 0.3175510204 t = -0.389690979 + 0.3175510204 Combine like terms: -0.389690979 + 0.3175510204 = -0.0721399586 t = -0.0721399586 Simplifying t = -0.0721399586Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.7072419994, -0.0721399586}
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