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Simplifying t2 + 17t + 14 = 0 Reorder the terms: 14 + 17t + t2 = 0 Solving 14 + 17t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 17t + -14 + t2 = 0 + -14 Reorder the terms: 14 + -14 + 17t + t2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 17t + t2 = 0 + -14 17t + t2 = 0 + -14 Combine like terms: 0 + -14 = -14 17t + t2 = -14 The t term is 17t. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17t + 72.25 + t2 = -14 + 72.25 Reorder the terms: 72.25 + 17t + t2 = -14 + 72.25 Combine like terms: -14 + 72.25 = 58.25 72.25 + 17t + t2 = 58.25 Factor a perfect square on the left side: (t + 8.5)(t + 8.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (t + 8.5) equal to 7.632168761 and -7.632168761.Subproblem 1
t + 8.5 = 7.632168761 Simplifying t + 8.5 = 7.632168761 Reorder the terms: 8.5 + t = 7.632168761 Solving 8.5 + t = 7.632168761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + t = 7.632168761 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + t = 7.632168761 + -8.5 t = 7.632168761 + -8.5 Combine like terms: 7.632168761 + -8.5 = -0.867831239 t = -0.867831239 Simplifying t = -0.867831239Subproblem 2
t + 8.5 = -7.632168761 Simplifying t + 8.5 = -7.632168761 Reorder the terms: 8.5 + t = -7.632168761 Solving 8.5 + t = -7.632168761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + t = -7.632168761 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + t = -7.632168761 + -8.5 t = -7.632168761 + -8.5 Combine like terms: -7.632168761 + -8.5 = -16.132168761 t = -16.132168761 Simplifying t = -16.132168761Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.867831239, -16.132168761}
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