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Simplifying -15t2 + -6t + 5 = 0 Reorder the terms: 5 + -6t + -15t2 = 0 Solving 5 + -6t + -15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.3333333333 + 0.4t + t2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.4t + 0.3333333333 + t2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.4t + t2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.4t + t2 = 0 + 0.3333333333 0.4t + t2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.4t + t2 = 0.3333333333 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 0.3333333333 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 0.3333333333 + 0.04 Combine like terms: 0.3333333333 + 0.04 = 0.3733333333 0.04 + 0.4t + t2 = 0.3733333333 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 0.3733333333 Calculate the square root of the right side: 0.611010093 Break this problem into two subproblems by setting (t + 0.2) equal to 0.611010093 and -0.611010093.Subproblem 1
t + 0.2 = 0.611010093 Simplifying t + 0.2 = 0.611010093 Reorder the terms: 0.2 + t = 0.611010093 Solving 0.2 + t = 0.611010093 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 0.611010093 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 0.611010093 + -0.2 t = 0.611010093 + -0.2 Combine like terms: 0.611010093 + -0.2 = 0.411010093 t = 0.411010093 Simplifying t = 0.411010093Subproblem 2
t + 0.2 = -0.611010093 Simplifying t + 0.2 = -0.611010093 Reorder the terms: 0.2 + t = -0.611010093 Solving 0.2 + t = -0.611010093 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -0.611010093 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -0.611010093 + -0.2 t = -0.611010093 + -0.2 Combine like terms: -0.611010093 + -0.2 = -0.811010093 t = -0.811010093 Simplifying t = -0.811010093Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.411010093, -0.811010093}
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