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Simplifying t2 + 15t + 40 = 0 Reorder the terms: 40 + 15t + t2 = 0 Solving 40 + 15t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 15t + -40 + t2 = 0 + -40 Reorder the terms: 40 + -40 + 15t + t2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 15t + t2 = 0 + -40 15t + t2 = 0 + -40 Combine like terms: 0 + -40 = -40 15t + t2 = -40 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 = -40 + 56.25 Reorder the terms: 56.25 + 15t + t2 = -40 + 56.25 Combine like terms: -40 + 56.25 = 16.25 56.25 + 15t + t2 = 16.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (t + 7.5) equal to 4.031128874 and -4.031128874.Subproblem 1
t + 7.5 = 4.031128874 Simplifying t + 7.5 = 4.031128874 Reorder the terms: 7.5 + t = 4.031128874 Solving 7.5 + t = 4.031128874 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 = 4.031128874 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 4.031128874 + -7.5 t = 4.031128874 + -7.5 Combine like terms: 4.031128874 + -7.5 = -3.468871126 t = -3.468871126 Simplifying t = -3.468871126Subproblem 2
t + 7.5 = -4.031128874 Simplifying t + 7.5 = -4.031128874 Reorder the terms: 7.5 + t = -4.031128874 Solving 7.5 + t = -4.031128874 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 = -4.031128874 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -4.031128874 + -7.5 t = -4.031128874 + -7.5 Combine like terms: -4.031128874 + -7.5 = -11.531128874 t = -11.531128874 Simplifying t = -11.531128874Solution
The solution to the problem is based on the solutions from the subproblems. t = {-3.468871126, -11.531128874}
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