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Simplifying 0.5t2 + 25t + -40 = 0 Reorder the terms: -40 + 25t + 0.5t2 = 0 Solving -40 + 25t + 0.5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -80 + 50t + t2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 50t + 80 + t2 = 0 + 80 Reorder the terms: -80 + 80 + 50t + t2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 50t + t2 = 0 + 80 50t + t2 = 0 + 80 Combine like terms: 0 + 80 = 80 50t + t2 = 80 The t term is 50t. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50t + 625 + t2 = 80 + 625 Reorder the terms: 625 + 50t + t2 = 80 + 625 Combine like terms: 80 + 625 = 705 625 + 50t + t2 = 705 Factor a perfect square on the left side: (t + 25)(t + 25) = 705 Calculate the square root of the right side: 26.551836095 Break this problem into two subproblems by setting (t + 25) equal to 26.551836095 and -26.551836095.Subproblem 1
t + 25 = 26.551836095 Simplifying t + 25 = 26.551836095 Reorder the terms: 25 + t = 26.551836095 Solving 25 + t = 26.551836095 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = 26.551836095 + -25 Combine like terms: 25 + -25 = 0 0 + t = 26.551836095 + -25 t = 26.551836095 + -25 Combine like terms: 26.551836095 + -25 = 1.551836095 t = 1.551836095 Simplifying t = 1.551836095Subproblem 2
t + 25 = -26.551836095 Simplifying t + 25 = -26.551836095 Reorder the terms: 25 + t = -26.551836095 Solving 25 + t = -26.551836095 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = -26.551836095 + -25 Combine like terms: 25 + -25 = 0 0 + t = -26.551836095 + -25 t = -26.551836095 + -25 Combine like terms: -26.551836095 + -25 = -51.551836095 t = -51.551836095 Simplifying t = -51.551836095Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.551836095, -51.551836095}
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