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Simplifying t2 + 19t + -8 = 0 Reorder the terms: -8 + 19t + t2 = 0 Solving -8 + 19t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 19t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 19t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 19t + t2 = 0 + 8 19t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 19t + t2 = 8 The t term is 19t. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19t + 90.25 + t2 = 8 + 90.25 Reorder the terms: 90.25 + 19t + t2 = 8 + 90.25 Combine like terms: 8 + 90.25 = 98.25 90.25 + 19t + t2 = 98.25 Factor a perfect square on the left side: (t + 9.5)(t + 9.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (t + 9.5) equal to 9.912113801 and -9.912113801.Subproblem 1
t + 9.5 = 9.912113801 Simplifying t + 9.5 = 9.912113801 Reorder the terms: 9.5 + t = 9.912113801 Solving 9.5 + t = 9.912113801 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + t = 9.912113801 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + t = 9.912113801 + -9.5 t = 9.912113801 + -9.5 Combine like terms: 9.912113801 + -9.5 = 0.412113801 t = 0.412113801 Simplifying t = 0.412113801Subproblem 2
t + 9.5 = -9.912113801 Simplifying t + 9.5 = -9.912113801 Reorder the terms: 9.5 + t = -9.912113801 Solving 9.5 + t = -9.912113801 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + t = -9.912113801 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + t = -9.912113801 + -9.5 t = -9.912113801 + -9.5 Combine like terms: -9.912113801 + -9.5 = -19.412113801 t = -19.412113801 Simplifying t = -19.412113801Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.412113801, -19.412113801}
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