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Simplifying 4.6t2 + -5.8t + -4.931 = 0 Reorder the terms: -4.931 + -5.8t + 4.6t2 = 0 Solving -4.931 + -5.8t + 4.6t2 = 0 Solving for variable 't'. 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 = 1.8426247585 t = 1.8426247585 Simplifying t = 1.8426247585Subproblem 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 = -0.5817551935 t = -0.5817551935 Simplifying t = -0.5817551935Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.8426247585, -0.5817551935}
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