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Simplifying 4.931 = 5.8t + 4.6t2 Solving 4.931 = 5.8t + 4.6t2 Solving for variable 't'. Reorder the terms: 4.931 + -5.8t + -4.6t2 = 5.8t + -5.8t + 4.6t2 + -4.6t2 Combine like terms: 5.8t + -5.8t = 0.0 4.931 + -5.8t + -4.6t2 = 0.0 + 4.6t2 + -4.6t2 4.931 + -5.8t + -4.6t2 = 4.6t2 + -4.6t2 Combine like terms: 4.6t2 + -4.6t2 = 0.0 4.931 + -5.8t + -4.6t2 = 0.0 Begin completing the square. Divide all terms by -4.6 the coefficient of the squared term: Divide each side by '-4.6'. -1.071956522 + 1.260869565t + t2 = 0 Move the constant term to the right: Add '1.071956522' to each side of the equation. -1.071956522 + 1.260869565t + 1.071956522 + t2 = 0 + 1.071956522 Reorder the terms: -1.071956522 + 1.071956522 + 1.260869565t + t2 = 0 + 1.071956522 Combine like terms: -1.071956522 + 1.071956522 = 0.000000000 0.000000000 + 1.260869565t + t2 = 0 + 1.071956522 1.260869565t + t2 = 0 + 1.071956522 Combine like terms: 0 + 1.071956522 = 1.071956522 1.260869565t + t2 = 1.071956522 The t term is 1.260869565t. Take half its coefficient (0.6304347825). Square it (0.3974480150) and add it to both sides. Add '0.3974480150' to each side of the equation. 1.260869565t + 0.3974480150 + t2 = 1.071956522 + 0.3974480150 Reorder the terms: 0.3974480150 + 1.260869565t + t2 = 1.071956522 + 0.3974480150 Combine like terms: 1.071956522 + 0.3974480150 = 1.469404537 0.3974480150 + 1.260869565t + t2 = 1.469404537 Factor a perfect square on the left side: (t + 0.6304347825)(t + 0.6304347825) = 1.469404537 Calculate the square root of the right side: 1.212189976 Break this problem into two subproblems by setting (t + 0.6304347825) equal to 1.212189976 and -1.212189976.Subproblem 1
t + 0.6304347825 = 1.212189976 Simplifying t + 0.6304347825 = 1.212189976 Reorder the terms: 0.6304347825 + t = 1.212189976 Solving 0.6304347825 + t = 1.212189976 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6304347825' to each side of the equation. 0.6304347825 + -0.6304347825 + t = 1.212189976 + -0.6304347825 Combine like terms: 0.6304347825 + -0.6304347825 = 0.0000000000 0.0000000000 + t = 1.212189976 + -0.6304347825 t = 1.212189976 + -0.6304347825 Combine like terms: 1.212189976 + -0.6304347825 = 0.5817551935 t = 0.5817551935 Simplifying t = 0.5817551935Subproblem 2
t + 0.6304347825 = -1.212189976 Simplifying t + 0.6304347825 = -1.212189976 Reorder the terms: 0.6304347825 + t = -1.212189976 Solving 0.6304347825 + t = -1.212189976 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6304347825' to each side of the equation. 0.6304347825 + -0.6304347825 + t = -1.212189976 + -0.6304347825 Combine like terms: 0.6304347825 + -0.6304347825 = 0.0000000000 0.0000000000 + t = -1.212189976 + -0.6304347825 t = -1.212189976 + -0.6304347825 Combine like terms: -1.212189976 + -0.6304347825 = -1.8426247585 t = -1.8426247585 Simplifying t = -1.8426247585Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.5817551935, -1.8426247585}
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