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Simplifying 0 = -0.09t2 + 0.9t + 2 Reorder the terms: 0 = 2 + 0.9t + -0.09t2 Solving 0 = 2 + 0.9t + -0.09t2 Solving for variable 't'. Combine like terms: 0 + -2 = -2 -2 + -0.9t + 0.09t2 = 2 + 0.9t + -0.09t2 + -2 + -0.9t + 0.09t2 Reorder the terms: -2 + -0.9t + 0.09t2 = 2 + -2 + 0.9t + -0.9t + -0.09t2 + 0.09t2 Combine like terms: 2 + -2 = 0 -2 + -0.9t + 0.09t2 = 0 + 0.9t + -0.9t + -0.09t2 + 0.09t2 -2 + -0.9t + 0.09t2 = 0.9t + -0.9t + -0.09t2 + 0.09t2 Combine like terms: 0.9t + -0.9t = 0.0 -2 + -0.9t + 0.09t2 = 0.0 + -0.09t2 + 0.09t2 -2 + -0.9t + 0.09t2 = -0.09t2 + 0.09t2 Combine like terms: -0.09t2 + 0.09t2 = 0.00 -2 + -0.9t + 0.09t2 = 0.00 Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. -22.22222222 + -10t + t2 = 0 Move the constant term to the right: Add '22.22222222' to each side of the equation. -22.22222222 + -10t + 22.22222222 + t2 = 0 + 22.22222222 Reorder the terms: -22.22222222 + 22.22222222 + -10t + t2 = 0 + 22.22222222 Combine like terms: -22.22222222 + 22.22222222 = 0.00000000 0.00000000 + -10t + t2 = 0 + 22.22222222 -10t + t2 = 0 + 22.22222222 Combine like terms: 0 + 22.22222222 = 22.22222222 -10t + t2 = 22.22222222 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 22.22222222 + 25 Reorder the terms: 25 + -10t + t2 = 22.22222222 + 25 Combine like terms: 22.22222222 + 25 = 47.22222222 25 + -10t + t2 = 47.22222222 Factor a perfect square on the left side: (t + -5)(t + -5) = 47.22222222 Calculate the square root of the right side: 6.871842709 Break this problem into two subproblems by setting (t + -5) equal to 6.871842709 and -6.871842709.Subproblem 1
t + -5 = 6.871842709 Simplifying t + -5 = 6.871842709 Reorder the terms: -5 + t = 6.871842709 Solving -5 + t = 6.871842709 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 6.871842709 + 5 Combine like terms: -5 + 5 = 0 0 + t = 6.871842709 + 5 t = 6.871842709 + 5 Combine like terms: 6.871842709 + 5 = 11.871842709 t = 11.871842709 Simplifying t = 11.871842709Subproblem 2
t + -5 = -6.871842709 Simplifying t + -5 = -6.871842709 Reorder the terms: -5 + t = -6.871842709 Solving -5 + t = -6.871842709 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -6.871842709 + 5 Combine like terms: -5 + 5 = 0 0 + t = -6.871842709 + 5 t = -6.871842709 + 5 Combine like terms: -6.871842709 + 5 = -1.871842709 t = -1.871842709 Simplifying t = -1.871842709Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.871842709, -1.871842709}
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