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Simplifying 22 = 39t + -5t2 Solving 22 = 39t + -5t2 Solving for variable 't'. Reorder the terms: 22 + -39t + 5t2 = 39t + -39t + -5t2 + 5t2 Combine like terms: 39t + -39t = 0 22 + -39t + 5t2 = 0 + -5t2 + 5t2 22 + -39t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 22 + -39t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4.4 + -7.8t + t2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + -7.8t + -4.4 + t2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + -7.8t + t2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + -7.8t + t2 = 0 + -4.4 -7.8t + t2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 -7.8t + t2 = -4.4 The t term is -7.8t. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8t + 15.21 + t2 = -4.4 + 15.21 Reorder the terms: 15.21 + -7.8t + t2 = -4.4 + 15.21 Combine like terms: -4.4 + 15.21 = 10.81 15.21 + -7.8t + t2 = 10.81 Factor a perfect square on the left side: (t + -3.9)(t + -3.9) = 10.81 Calculate the square root of the right side: 3.287856445 Break this problem into two subproblems by setting (t + -3.9) equal to 3.287856445 and -3.287856445.Subproblem 1
t + -3.9 = 3.287856445 Simplifying t + -3.9 = 3.287856445 Reorder the terms: -3.9 + t = 3.287856445 Solving -3.9 + t = 3.287856445 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + t = 3.287856445 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + t = 3.287856445 + 3.9 t = 3.287856445 + 3.9 Combine like terms: 3.287856445 + 3.9 = 7.187856445 t = 7.187856445 Simplifying t = 7.187856445Subproblem 2
t + -3.9 = -3.287856445 Simplifying t + -3.9 = -3.287856445 Reorder the terms: -3.9 + t = -3.287856445 Solving -3.9 + t = -3.287856445 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + t = -3.287856445 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + t = -3.287856445 + 3.9 t = -3.287856445 + 3.9 Combine like terms: -3.287856445 + 3.9 = 0.612143555 t = 0.612143555 Simplifying t = 0.612143555Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.187856445, 0.612143555}
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