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Simplifying 13 = 55t + -5t2 Solving 13 = 55t + -5t2 Solving for variable 't'. Reorder the terms: 13 + -55t + 5t2 = 55t + -55t + -5t2 + 5t2 Combine like terms: 55t + -55t = 0 13 + -55t + 5t2 = 0 + -5t2 + 5t2 13 + -55t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 13 + -55t + 5t2 = 0 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 = 27.65 30.25 + -11t + t2 = 27.65 Factor a perfect square on the left side: (t + -5.5)(t + -5.5) = 27.65 Calculate the square root of the right side: 5.25832673 Break this problem into two subproblems by setting (t + -5.5) equal to 5.25832673 and -5.25832673.Subproblem 1
t + -5.5 = 5.25832673 Simplifying t + -5.5 = 5.25832673 Reorder the terms: -5.5 + t = 5.25832673 Solving -5.5 + t = 5.25832673 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 = 5.25832673 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = 5.25832673 + 5.5 t = 5.25832673 + 5.5 Combine like terms: 5.25832673 + 5.5 = 10.75832673 t = 10.75832673 Simplifying t = 10.75832673Subproblem 2
t + -5.5 = -5.25832673 Simplifying t + -5.5 = -5.25832673 Reorder the terms: -5.5 + t = -5.25832673 Solving -5.5 + t = -5.25832673 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 = -5.25832673 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + t = -5.25832673 + 5.5 t = -5.25832673 + 5.5 Combine like terms: -5.25832673 + 5.5 = 0.24167327 t = 0.24167327 Simplifying t = 0.24167327Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.75832673, 0.24167327}
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