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Simplifying 5t2 + 30t + 4 = 0 Reorder the terms: 4 + 30t + 5t2 = 0 Solving 4 + 30t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 6t + t2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 6t + -0.8 + t2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 6t + t2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 6t + t2 = 0 + -0.8 6t + t2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 6t + t2 = -0.8 The t term is 6t. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6t + 9 + t2 = -0.8 + 9 Reorder the terms: 9 + 6t + t2 = -0.8 + 9 Combine like terms: -0.8 + 9 = 8.2 9 + 6t + t2 = 8.2 Factor a perfect square on the left side: (t + 3)(t + 3) = 8.2 Calculate the square root of the right side: 2.863564213 Break this problem into two subproblems by setting (t + 3) equal to 2.863564213 and -2.863564213.Subproblem 1
t + 3 = 2.863564213 Simplifying t + 3 = 2.863564213 Reorder the terms: 3 + t = 2.863564213 Solving 3 + t = 2.863564213 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 2.863564213 + -3 Combine like terms: 3 + -3 = 0 0 + t = 2.863564213 + -3 t = 2.863564213 + -3 Combine like terms: 2.863564213 + -3 = -0.136435787 t = -0.136435787 Simplifying t = -0.136435787Subproblem 2
t + 3 = -2.863564213 Simplifying t + 3 = -2.863564213 Reorder the terms: 3 + t = -2.863564213 Solving 3 + t = -2.863564213 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = -2.863564213 + -3 Combine like terms: 3 + -3 = 0 0 + t = -2.863564213 + -3 t = -2.863564213 + -3 Combine like terms: -2.863564213 + -3 = -5.863564213 t = -5.863564213 Simplifying t = -5.863564213Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.136435787, -5.863564213}
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