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Simplifying t2 + 50t + -35 = 0 Reorder the terms: -35 + 50t + t2 = 0 Solving -35 + 50t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 50t + 35 + t2 = 0 + 35 Reorder the terms: -35 + 35 + 50t + t2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 50t + t2 = 0 + 35 50t + t2 = 0 + 35 Combine like terms: 0 + 35 = 35 50t + t2 = 35 The t term is 50t. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50t + 625 + t2 = 35 + 625 Reorder the terms: 625 + 50t + t2 = 35 + 625 Combine like terms: 35 + 625 = 660 625 + 50t + t2 = 660 Factor a perfect square on the left side: (t + 25)(t + 25) = 660 Calculate the square root of the right side: 25.690465157 Break this problem into two subproblems by setting (t + 25) equal to 25.690465157 and -25.690465157.Subproblem 1
t + 25 = 25.690465157 Simplifying t + 25 = 25.690465157 Reorder the terms: 25 + t = 25.690465157 Solving 25 + t = 25.690465157 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = 25.690465157 + -25 Combine like terms: 25 + -25 = 0 0 + t = 25.690465157 + -25 t = 25.690465157 + -25 Combine like terms: 25.690465157 + -25 = 0.690465157 t = 0.690465157 Simplifying t = 0.690465157Subproblem 2
t + 25 = -25.690465157 Simplifying t + 25 = -25.690465157 Reorder the terms: 25 + t = -25.690465157 Solving 25 + t = -25.690465157 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = -25.690465157 + -25 Combine like terms: 25 + -25 = 0 0 + t = -25.690465157 + -25 t = -25.690465157 + -25 Combine like terms: -25.690465157 + -25 = -50.690465157 t = -50.690465157 Simplifying t = -50.690465157Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.690465157, -50.690465157}
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