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Simplifying 55t + -5t2 + 13 = 0 Reorder the terms: 13 + 55t + -5t2 = 0 Solving 13 + 55t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.6 + -11t + t2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -11t + 2.6 + t2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -11t + t2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -11t + t2 = 0 + 2.6 -11t + t2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -11t + t2 = 2.6 The t term is -11t. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11t + 30.25 + t2 = 2.6 + 30.25 Reorder the terms: 30.25 + -11t + t2 = 2.6 + 30.25 Combine like terms: 2.6 + 30.25 = 32.85 30.25 + -11t + t2 = 32.85 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 32.85 Calculate the square root of the right side: 5.731491952 Break this problem into two subproblems by setting (t + -5.5) equal to 5.731491952 and -5.731491952.Subproblem 1
t + -5.5 = 5.731491952 Simplifying t + -5.5 = 5.731491952 Reorder the terms: -5.5 + t = 5.731491952 Solving -5.5 + t = 5.731491952 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = 5.731491952 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 5.731491952 + 5.5 t = 5.731491952 + 5.5 Combine like terms: 5.731491952 + 5.5 = 11.231491952 t = 11.231491952 Simplifying t = 11.231491952Subproblem 2
t + -5.5 = -5.731491952 Simplifying t + -5.5 = -5.731491952 Reorder the terms: -5.5 + t = -5.731491952 Solving -5.5 + t = -5.731491952 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + t = -5.731491952 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -5.731491952 + 5.5 t = -5.731491952 + 5.5 Combine like terms: -5.731491952 + 5.5 = -0.231491952 t = -0.231491952 Simplifying t = -0.231491952Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.231491952, -0.231491952}
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