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Simplifying -4.5t2 + 43t + 2 = 0 Reorder the terms: 2 + 43t + -4.5t2 = 0 Solving 2 + 43t + -4.5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.5 the coefficient of the squared term: Divide each side by '-4.5'. -0.4444444444 + -9.555555556t + t2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -9.555555556t + 0.4444444444 + t2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -9.555555556t + t2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -9.555555556t + t2 = 0 + 0.4444444444 -9.555555556t + t2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -9.555555556t + t2 = 0.4444444444 The t term is -9.555555556t. Take half its coefficient (-4.777777778). Square it (22.82716050) and add it to both sides. Add '22.82716050' to each side of the equation. -9.555555556t + 22.82716050 + t2 = 0.4444444444 + 22.82716050 Reorder the terms: 22.82716050 + -9.555555556t + t2 = 0.4444444444 + 22.82716050 Combine like terms: 0.4444444444 + 22.82716050 = 23.2716049444 22.82716050 + -9.555555556t + t2 = 23.2716049444 Factor a perfect square on the left side: (t + -4.777777778)(t + -4.777777778) = 23.2716049444 Calculate the square root of the right side: 4.824065189 Break this problem into two subproblems by setting (t + -4.777777778) equal to 4.824065189 and -4.824065189.Subproblem 1
t + -4.777777778 = 4.824065189 Simplifying t + -4.777777778 = 4.824065189 Reorder the terms: -4.777777778 + t = 4.824065189 Solving -4.777777778 + t = 4.824065189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.777777778' to each side of the equation. -4.777777778 + 4.777777778 + t = 4.824065189 + 4.777777778 Combine like terms: -4.777777778 + 4.777777778 = 0.000000000 0.000000000 + t = 4.824065189 + 4.777777778 t = 4.824065189 + 4.777777778 Combine like terms: 4.824065189 + 4.777777778 = 9.601842967 t = 9.601842967 Simplifying t = 9.601842967Subproblem 2
t + -4.777777778 = -4.824065189 Simplifying t + -4.777777778 = -4.824065189 Reorder the terms: -4.777777778 + t = -4.824065189 Solving -4.777777778 + t = -4.824065189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.777777778' to each side of the equation. -4.777777778 + 4.777777778 + t = -4.824065189 + 4.777777778 Combine like terms: -4.777777778 + 4.777777778 = 0.000000000 0.000000000 + t = -4.824065189 + 4.777777778 t = -4.824065189 + 4.777777778 Combine like terms: -4.824065189 + 4.777777778 = -0.046287411 t = -0.046287411 Simplifying t = -0.046287411Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.601842967, -0.046287411}
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