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Simplifying 26 = 54t + -5t2 Solving 26 = 54t + -5t2 Solving for variable 't'. Reorder the terms: 26 + -54t + 5t2 = 54t + -54t + -5t2 + 5t2 Combine like terms: 54t + -54t = 0 26 + -54t + 5t2 = 0 + -5t2 + 5t2 26 + -54t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 26 + -54t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.2 + -10.8t + t2 = 0 Move the constant term to the right: Add '-5.2' to each side of the equation. 5.2 + -10.8t + -5.2 + t2 = 0 + -5.2 Reorder the terms: 5.2 + -5.2 + -10.8t + t2 = 0 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + -10.8t + t2 = 0 + -5.2 -10.8t + t2 = 0 + -5.2 Combine like terms: 0 + -5.2 = -5.2 -10.8t + t2 = -5.2 The t term is -10.8t. Take half its coefficient (-5.4). Square it (29.16) and add it to both sides. Add '29.16' to each side of the equation. -10.8t + 29.16 + t2 = -5.2 + 29.16 Reorder the terms: 29.16 + -10.8t + t2 = -5.2 + 29.16 Combine like terms: -5.2 + 29.16 = 23.96 29.16 + -10.8t + t2 = 23.96 Factor a perfect square on the left side: (t + -5.4)(t + -5.4) = 23.96 Calculate the square root of the right side: 4.8948953 Break this problem into two subproblems by setting (t + -5.4) equal to 4.8948953 and -4.8948953.Subproblem 1
t + -5.4 = 4.8948953 Simplifying t + -5.4 = 4.8948953 Reorder the terms: -5.4 + t = 4.8948953 Solving -5.4 + t = 4.8948953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + t = 4.8948953 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + t = 4.8948953 + 5.4 t = 4.8948953 + 5.4 Combine like terms: 4.8948953 + 5.4 = 10.2948953 t = 10.2948953 Simplifying t = 10.2948953Subproblem 2
t + -5.4 = -4.8948953 Simplifying t + -5.4 = -4.8948953 Reorder the terms: -5.4 + t = -4.8948953 Solving -5.4 + t = -4.8948953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.4' to each side of the equation. -5.4 + 5.4 + t = -4.8948953 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + t = -4.8948953 + 5.4 t = -4.8948953 + 5.4 Combine like terms: -4.8948953 + 5.4 = 0.5051047 t = 0.5051047 Simplifying t = 0.5051047Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.2948953, 0.5051047}
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