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Simplifying t2 + 15t + 16 = 0 Reorder the terms: 16 + 15t + t2 = 0 Solving 16 + 15t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 15t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + 15t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 15t + t2 = 0 + -16 15t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 15t + t2 = -16 The t term is 15t. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15t + 56.25 + t2 = -16 + 56.25 Reorder the terms: 56.25 + 15t + t2 = -16 + 56.25 Combine like terms: -16 + 56.25 = 40.25 56.25 + 15t + t2 = 40.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (t + 7.5) equal to 6.34428877 and -6.34428877.Subproblem 1
t + 7.5 = 6.34428877 Simplifying t + 7.5 = 6.34428877 Reorder the terms: 7.5 + t = 6.34428877 Solving 7.5 + t = 6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = 6.34428877 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 6.34428877 + -7.5 t = 6.34428877 + -7.5 Combine like terms: 6.34428877 + -7.5 = -1.15571123 t = -1.15571123 Simplifying t = -1.15571123Subproblem 2
t + 7.5 = -6.34428877 Simplifying t + 7.5 = -6.34428877 Reorder the terms: 7.5 + t = -6.34428877 Solving 7.5 + t = -6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = -6.34428877 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -6.34428877 + -7.5 t = -6.34428877 + -7.5 Combine like terms: -6.34428877 + -7.5 = -13.84428877 t = -13.84428877 Simplifying t = -13.84428877Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.15571123, -13.84428877}
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