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Simplifying t2 + 15t = -11 Reorder the terms: 15t + t2 = -11 Solving 15t + t2 = -11 Solving for variable 't'. Reorder the terms: 11 + 15t + t2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + 15t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 15t + -11 + t2 = 0 + -11 Reorder the terms: 11 + -11 + 15t + t2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 15t + t2 = 0 + -11 15t + t2 = 0 + -11 Combine like terms: 0 + -11 = -11 15t + t2 = -11 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 = -11 + 56.25 Reorder the terms: 56.25 + 15t + t2 = -11 + 56.25 Combine like terms: -11 + 56.25 = 45.25 56.25 + 15t + t2 = 45.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (t + 7.5) equal to 6.726812024 and -6.726812024.Subproblem 1
t + 7.5 = 6.726812024 Simplifying t + 7.5 = 6.726812024 Reorder the terms: 7.5 + t = 6.726812024 Solving 7.5 + t = 6.726812024 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 = 6.726812024 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 6.726812024 + -7.5 t = 6.726812024 + -7.5 Combine like terms: 6.726812024 + -7.5 = -0.773187976 t = -0.773187976 Simplifying t = -0.773187976Subproblem 2
t + 7.5 = -6.726812024 Simplifying t + 7.5 = -6.726812024 Reorder the terms: 7.5 + t = -6.726812024 Solving 7.5 + t = -6.726812024 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 = -6.726812024 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -6.726812024 + -7.5 t = -6.726812024 + -7.5 Combine like terms: -6.726812024 + -7.5 = -14.226812024 t = -14.226812024 Simplifying t = -14.226812024Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.773187976, -14.226812024}
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